DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES

DEIAS

Differential Equations In Abstract Spaces

DEPARTAMENTO COMPUTAÇÃO E MATEMÁTICA - FFCLRP

USP

DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES

We are interested in answering questions related to the existence, uniqueness, stability, periodicity and qualitative properties for differential equations in abstract spaces. Specifically, we study models with impulsive differential equations, state-dependent delay differential equations, neutral differential equations, fractional differential equations, among others. In addition, we investigate the numerical solution of this type of equations and their application in Economic models.

Seminars

Upcoming

No future events

Past

Well posedness and qualitative analysis of a SEIR model with spatial diffusion
Speaker: José Paulo Carvalho dos Santos - Universidade Federal de Alfenas, Brasil
07/10/2022 - 13:00 - 15:00

On resolvent families and its applications to the existence of mild solutions to differential equations
Speaker: Rodrigo Ponce - Universidad de Talca, Chile
04/06/2021 - 13:45 - 15:45

An Introduction to the Differential inclusions
Speaker: Jacson Simsen - Universidade Federal de Itajubá, Brasil
28/05/2021 - 13:45 - 15:45

Uniform approximation of an impulsive Hopfield cellular neural network by using a piecewise constant argument
Speaker: Manuel Pinto and Ricardo Torres - Universidad de Chile, Chile
14/05/2021 - 13:45 - 15:45

Members

 

Eduardo Hernandez
Eduardo Hernandez

CV Lattes
Google scholar
lalohm@ffclrp.usp.br
Research line: Existence and qualitative properties of solution in neutral equations with delay depending on the state; application in traveling waves of partial differential equations.

Katia Azevedo
Katia Azevedo

CV Lattes
Google scholar
kandreia@ffclrp.usp.br
Research line: Delay differential equations.

Michelle Pierri
Michelle Pierri

CV Lattes
Google scholar
michellepierri@ffclrp.usp.br
Research line: functional differential equations; quasi-periodicity

Vanessa Rolnik
Vanessa Rolnik

CV Lattes
Google scholar
vanessarolnik@ffclrp.usp.br
Research line: approximation of solution for delay differential equations

External Members

Andréa Prokopczyk
Andréa Prokopczyk

Institution: UNESP São José do Rio Preto, Brazil
Research line: Differential Equations, control Theory

Donal O’Regan
Donal O’Regan

Institution: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Research line: Nonlinear analysis, Fixed point theory

Jianhong Wu
Jianhong Wu

Institution: York University, Toronto, Canada
Research line: Delay differential equations, systems neural, disease

José Paulo Carvalho dos Santos
José Paulo Carvalho dos Santos

Institution: Universidade Federal de Alfenas, Brazil
Research line: Functional differential equations, fractional differential equations, Mathematical Biology

Marta Cilene Gadotti
Marta Cilene Gadotti

Institution: UNESP Rio Claro, Brazil
Research line: Delay differential equation, periodic solutions, impulses, orbital stability

Sergei Trofimchuk
Sergei Trofimchuk

Institution: Universidad de Talca, Chile
Research line: Differential equations, difference equations, dynamical systems

Postdoctoral Researchers

Denis Fernandes da Silva
Denis Fernandes da Silva

Postdoctoral Researcher

Sumit Arora
Sumit Arora

Postdoctoral Researcher

Doctoral Students

Shashank Pandey
Shashank Pandey

Doctoral Student

Department of Mathematics, Indian Institute of Technology Roorkee

Vinicius Vitório
Vinicius Vitório

Doctoral Student

Unesp - São José de Rio Preto

Master Students

Ana Carolina Souza Melega
Ana Carolina Souza Melega

Master Student

Master program in Mathematics – DCM – FFCLRP/USP
Supervising professor :Michelle Pierri

Carolina Pereira Neves
Carolina Pereira Neves

Master Student

Master program in Mathematics – DCM – FFCLRP/USP
Supervising professor :Katia Azevedo

Edmara Viana da Silva
Edmara Viana da Silva

Master Student
Equações diferenciais funcionais com memória dependendo do estado
Master program in Mathematics – DCM – FFCLRP/USP
Supervising professor :Eduardo Hernández

Juliano Rian Custodio Malta
Juliano Rian Custodio Malta

Master Student
O Teorema de Bifurcação de Hopf e aplicações em modelos econômicos
Master program in Mathematics – DCM – FFCLRP/USP
Supervising professor :Katia Azevedo

María José Ayala Bolagay
María José Ayala Bolagay

Master Student

Master program in Mathematics – DCM – FFCLRP/USP
Supervising professor :Eduardo Hernández

Sandro Luiz Santos Generoso Filho
Sandro Luiz Santos Generoso Filho

Master Student
Existência e aproximação numérica de soluções de modelos diferenciais na teoria de flutuações de preços
Master program in Applied Computation – DCM – FFCLRP/USP
Supervising professor :Eduardo Hernández

Undergraduate Students

Bruno Henrique de Sousa Mouro
Bruno Henrique de Sousa Mouro

Undergraduate Student
Modelagem Matemática

Débora Martins de Souza
Débora Martins de Souza

Undergraduate Student
Convergence of Numerical Solutions to Ordinary Differential Equations

Henrique Messias Corbi Lopes
Henrique Messias Corbi Lopes

Undergraduate Student

Juan Lucas da Rocha Silva
Juan Lucas da Rocha Silva

Undergraduate Student

Karoline Prospero Herculano da Silva
Karoline Prospero Herculano da Silva

Undergraduate Student
Métodos numéricos em equações diferenciais aplicados a negócios

Luis Guilherme Coelho Bueno
Luis Guilherme Coelho Bueno

Undergraduate Student

Rafael Francisco de Lima
Rafael Francisco de Lima

Undergraduate Student
Equações Diferenciais com Memória a Depender do Estado

Sabrina Sousa Carvalho
Sabrina Sousa Carvalho

Undergraduate Student
Métodos numéricos para autovalores e autovetores e aplicação à análise de dados multivariados

Vitória Barbosa Bueno
Vitória Barbosa Bueno

Undergraduate Student
Métodos numéricos para EDOs: um estudo sobre convergência

Former Students

 Denis Fernandes da Silva

Wellposedness and asymptotic behavior of solutions of abstract differential equations with state-dependent delay
Doctoral Thesis, 2021

https://doi.org/10.11606/T.55.2021.tde-24062021-115059
Orientador:

 Gabriel Fonseca Ament
Continuous Runge-Kutta method for delay differential equations and applications in population dynamics
Master's Dissertation, 2022

https://doi.org/10.11606/D.59.2022.tde-31102022-100226
Orientador:

 Lucas Lisboa Leão

Master's Dissertation, 2023


Orientador:

 Patrícia Kyoe Fukushima
Inverse problems associated with impulsive differential equations
Master's Dissertation, 2019

https://doi.org/10.11606/D.59.2019.tde-06042019-094255
Orientador:

 Thauana Marcela Ferrari Tertuliano
Solow equations with state-dependent delay
Master's Dissertation, 2021

https://doi.org/10.11606/D.59.2021.tde-24092021-154111
Orientador:

Recent publications

  1. HERNANDEZ, EDUARDO; ROLNIK, VANESSA ; FERRARI, THAUANA M. Existence and Uniqueness of Solutions for Abstract Integro-differential Equations with State-Dependent Delay and Applications.Mediterranean Journal of Mathematics, v. 19, p. 101, 2022
  2. HERNANDEZ, EDUARDOExistence and uniqueness of global solution for abstract second order differential equations with state-dependent delay. Mathematische Nachrichten, v. 295, p. 124-139, 2022
  3. HERNANDEZ, EDUARDO; FERNANDES, DENIS ; WU, JIANHONG.Existence and uniqueness of solutions, well- posedness and global attractor for abstract differential equations with state-dependent delay. JOURNAL OF DIFFERENTIAL EQUATIONS, v. 302, p. 753-806, 2021
  4. DEBBOUCHE, AMAR ; FEč ; HERNÁNDEZ, EDUARDO.Special issue: Latest computational methods on fractional dynamic systems -VSI fractional dynamic system.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v. 388, p. 113322, 2021
  5. DEBBOUCHE, AMAR, FECKAN, MICHAL, HERNÁNDEZ, EDUARDO.Special issue: Latest computational methods on fractional dynamic systemsJ. Comput. Appl. Math. 388 (2021), 113322, 2 pp,2021
  6. HERNÁNDEZ, EDUARDO; Michelle Pierri ; FERNANDES, D. ; LISBOA, L.Existence and uniqueness of solution for neutral differential equations with state- dependent delay.Journal of Fixed Point Theory and Applications, v. 23, p. 70, 2021
  7. EDUARDO HERNÁNDEZ, DENIS FERNANDES, JIANHONG WU.Well-posedness of abstract integro-differential equations with state-dependent delay.Proc. Amer. Math. Soc., 148, 1595-1609,2020
  8. EDUARDO HERNÁNDEZ, SERGEI TROFIMCHUK.Nonstandard quasi-monotonicity: an application to the wave existence in a neutral KPP-Fisher equation. Journal of Dynamics and Differential Equations, 32 , no. 2, 921-939,2020
  9. HERNÁNDEZ, EDUARDO; TROFIMCHUK, SERGEI .Traveling waves solutions for partial neutral differential equations.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v. 481, p. 123458,2020
  10. EDUARDO HERNANDEZ; JIANHONG WU, ALKA CHADHA.Existence, uniqueness and approximate controllability of abstract differential equations with state-dependent delay.J. Differential Equations, 269, 10, 8701-8735,2020
  11. E. HERNÁNDEZ, J. WU., D. FERNANDES.Existence and uniqueness of solutions for abstract neutral differential equations with state dependent delay. Applied Mathematics & Optimization, 81 , no. 1, 89-111,2020
  12. HERNÁNDEZ, EDUARDO. Abstract impulsive differential equations without predefined time impulses.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , v. 491, p. 124288, 2020
  13. HERNÁNDEZ, EDUARDO; TROFIMCHUK, SERGEI .Traveling waves solutions for partial neutral differential equations.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , v. 481, p. 123458,2020
  14. HERNÁNDEZ, EDUARDO.Abstract impulsive differential equations without predefined time impulses.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v. 491, p. 124288,2020
  15. HERNÁNDEZ, EDUARDO; AZEVEDO, KATIA A. G. ; GADOTTI, MARTA C. .Existence and uniqueness of solution for abstract differential equations with state-dependent delayed impulses.Journal of Fixed Point Theory and Applications, v. 21, p. 36,2019
  16. HERNÁNDEZ, EDUARDO; WU, JIANHONG .Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay.PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 62, p. 771-788,2019
  17. HERNÁNDEZ, EDUARDO; WU, JIANHONG .Existence and uniqueness of C^{1+\al}-strict solutions for integro- differential equations with state-dependent delay.Differential and Integral Equations, v. 32, p. 291-322,2019
  18. AZEVEDO, KATIA A. G..Existence and Uniqueness of Solution for Abstract Differential Equations with State-Dependent Time Impulses.Mediterranean Journal of Mathematics, v. 16, p. 42,2019
  19. HERNÁNDEZ, EDUARDO; WU, JIANHONG . Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay.PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY , v. 62, p. 771-788,2019
  20. HERNÁNDEZ, EDUARDO; WU, JIANHONG .Existence and uniqueness of C^{1+\al}-strict solutions for integro-differential equations with state-dependent delay. Differential and Integral Equations , v. 32, p. 291-322, 2019
  21. HERNÁNDEZ, EDUARDO; AZEVEDO, KATIA A. G. ; GADOTTI, MARTA C. .Existence and uniqueness of solution for abstract differential equations with state-dependent delayed impulses.Journal of Fixed Point Theory and Applications , v. 21, p. 36,2019
  22. HERNÁNDEZ, EDUARDO; TROFIMCHUK, SERGEI .Nonstandard Quasi- monotonicity: An Application to the Wave Existence in a Neutral KPP-Fisher Equation.Journal of Dynamics and Differential Equations , v. 32, p. 921-939,2019
  23. AZEVEDO, KATIA A. G..Existence and Uniqueness of Solution for Abstract Differential Equations with State-Dependent Time Impulses.Mediterranean Journal of Mathematics , v. 16, p. 42,2019
  24. HERNÁNDEZ, EDUARDO; TROFIMCHUK, SERGEI .Nonstandard Quasi-monotonicity: An Application to the Wave Existence in a Neutral KPP-Fisher Equation.Journal of Dynamics and Differential Equations, v. 32, p. 921- 939,2019
  25. HERNÁNDEZ, EDUARDO.On abstract differential equations with state dependent non-local conditions.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v. 466, p. 408-425,2018
  26. Eduardo Hernández, Michelle Pierri,Existence and uniqueness of $\bf\mathcal{S}$- asymptotically $\omega$-periodic solutions for abstract differential equations with state dependent delay. {\sl Bull. Aust. Math. Soc.} 98 , no. 3, 456-464,2018
  27. E; Hernández., J. Wu.Traveling wave front for partial neutral differential equations.{\sl Proc. Amer. Math. Soc. } 146 , 1603-1617,2018
  28. E., Hernández, D., O'Regan.Abstract differential equations with state dependent nonlocal conditions.{\sl Applied Mathematics Letters,} 83, 103-109.2018
  29. Hernandez, Eduardo; AZEVEDO, K. A. G. ; ROLNIK, V. . Wellposedness of abstract differential equations with state-dependent delay.Mathematische Nachrichten , v. 13, p. 2045-2056,2018
  30. Hernandez, Eduardo; WU, JIANHONG ; FERNANDES, D. Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State- Dependent Delay.APPLIED MATHEMATICS AND OPTIMIZATION , p. 89-111, 2018
  31. Hernandez, Eduardo; O'Regan, Donal. .On state dependent non-local conditions.APPLIED MATHEMATICS LETTERS , v. 83, p. 103-109,2018
  32. HERNÁNDEZ, EDUARDO; Pierri, Michelle .On abstract neutral differential equations with state-dependent delay.Journal of Fixed Point Theory and Applications , v. 20, p. 20:97, 2018
  33. HERNÁNDEZ, EDUARDO.On abstract differential equations with state dependent non-local conditions.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , v. 466, p. 408-425,2018
  34. HERNÁNDEZ, EDUARDO; Pierri, Michelle .-ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY.BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY , v. 2018, p. 456-464,2018
  35. Hernandez, Eduardo; AZEVEDO, K. A. G. ; ROLNIK, V. .Wellposedness of abstract differential equations with state-dependent delay.Mathematische Nachrichten, v. 13, p. 2045-2056,2018
  36. Hernandez, Eduardo; WU, JIANHONG ; FERNANDES, D. .Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay.APPLIED MATHEMATICS AND OPTIMIZATION, p. 89-111,2018
  37. Hernandez, Eduardo; O'Regan, Donal. .On state dependent non-local conditions.APPLIED MATHEMATICS LETTERS, v. 83, p. 103-109,2018
  38. HERNÁNDEZ, EDUARDO; Pierri, Michelle .On abstract neutral differential equations with state-dependent delay.Journal of Fixed Point Theory and Applications, v. 20, p. 20:97,2018
  39. HERNÁNDEZ, EDUARDO; Pierri, Michelle .ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY.BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, v. 2018, p. 456-464,2018
  40. SANTOS, JAIR SILVÉRIO DOS ; AZEVEDO, KATIA A. G. .Dynamics of Nonlinear Interactions among Forces with Lagged Effect.APPLIED MATHEMATICS, v. 08, p. 1437-1444,2017
  41. HERNÁNDEZ, EDUARDO; AZEVEDO, KATIA A. G. ; O?REGAN, DONAL .On second order differential equations with state-dependent delay.APPLICABLE ANALYSIS , v. 15, p. 2610-2617,2017
  42. HERNÁNDEZ, EDUARDO; AZEVEDO, KATIA A. G. ; O'REGAN, DONAL .On second order differential equations with state-dependent delay.APPLICABLE ANALYSIS, v. 15, p. 2610-2617,2017
  43. SANTOS, JAIR SILVÉRIO DOS ; AZEVEDO, KATIA A. G. .Dynamics of Nonlinear Interactions among Forces with Lagged Effect.APPLIED MATHEMATICS, v. 08, p. 1437-1444,2017
  44. HERNANDEZ, EDUARDO; WU, JIANHONG .Traveling wave front for partial neutral differential equations.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 146, p. 1603-1617,2017
  45. HERNANDEZ, EDUARDO; WU, JIANHONG .Traveling wave front for partial neutral differential equations.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY , v. 146, p. 1603-1617,2017
  46. HERNÁNDEZ, EDUARDO; O?REGAN, DONAL .On implicit abstract neutral nonlinear differential equations.Applied Mathematics & Optimization , v. 73, p. 329-347,2016
  47. PIERRI, Michelle ; OREGAN, D. .Some comments on the paper: Controllability of fractional neutral stochastic functional differential systems, Z.Angew. Math. Phys. 65 (2014), no. 5, 941-9592. Zeitschrift fur Angewandte Mathematik und Physik (Printed ed.) , v. 2015, p. 1-4,2016
  48. Hernán R. Henríquez ; PIERRI, Michelle ; Vanessa Rolnik .Pseudo S- asymptotically periodic solutions of second-order abstract Cauchy problems.Applied Mathematics and Computation , v. 2016, p. 590-603,2016
  49. HERNÁNDEZ, EDUARDO; O'REGAN, DONAL .On abstract degenerate neutral differential equations.Zeitschrift fur Angewandte Mathematik und Physik (Printed ed.), v. 67, p. 0044-2275/16/05,2016
  50. HERNÁNDEZ, EDUARDO; O'REGAN, DONAL .On a New Class of Abstract Neutral Integro-Differential Equations and Applications.ACTA APPLICANDAE MATHEMATICAE, v. 149, p. 125-137,2016
  51. PIERRI, Michelle ; OREGAN, D. ; Andréa Prokopczyk .On recent developments treating the exact controllability of abstract control problems.Electronic Journal of Differential Equations , v. 2016, p. 1-9,2016
  52. Hernán R. Henríquez ; PIERRI, Michelle ; Vanessa Rolnik .Pseudo S-asymptotically periodic solutions of second-order abstract Cauchy problems.Applied Mathematics and Computation, v. 2016, p. 590-603,2016
  53. PIERRI, Michelle ; OREGAN, D. .Some comments on the paper: Controllability of fractional neutral stochastic functional differential systems, Z. Angew.Math. Phys. 65 (2014), no. 5, 941-9592. Zeitschrift fur Angewandte Mathematik und Physik (Printed ed.), v. 2015, p. 1-4,2016
  54. PIERRI, Michelle ; OREGAN, D. ; Andréa Prokopczyk .On recent developments treating the exact controllability of abstract control problems.Electronic Journal of Differential Equations, v. 2016, p. 1-9,2016
  55. HERNÁNDEZ, EDUARDO; O'REGAN, DONAL .On implicit abstract neutral nonlinear differential equations.Applied Mathematics & Optimization, v. 73, p. 329-347,2016
  56. HERNANDEZ, EDUARDO; Pierri, Michelle ; WU, JIANHONG .C1+α-strict solutions and wellposedness of abstract differential equations with state dependent delay.Journal of Differential Equations (Print), v. 261, p. 6856- 6882,2016
  57. Hernández, Eduardo; O'Regan, Donal,On implicit abstract neutral nonlinear differential equations,{\sl Applied Mathematics $\&$ Optimization} 73 , (3) 329- 347.2016
  58. HERNÁNDEZ, EDUARDO; O?REGAN, DONAL .On a New Class of Abstract Neutral Integro-Differential Equations and Applications.ACTA APPLICANDAE MATHEMATICAE , v. 149, p. 125-137,2016
  59. HERNÁNDEZ, EDUARDO; O?REGAN, DONAL .On abstract degenerate neutral differential equations.Zeitschrift fur Angewandte Mathematik und Physik (Printed ed.) , v. 67, p. 0044-2275/16/05,2016
  60. HERNANDEZ, EDUARDO; Pierri, Michelle ; WU, JIANHONG .C1+α-strict solutions and wellposedness of abstract differential equations with state dependent delay.Journal of Differential Equations (Print) , v. 261, p. 6856- 6882,2016
  61. EDUARDO HERNÁNDEZ.Existence and uniqueness of global solution for abstract second order differential equations with state-dependent delay. To appear in Mathematische Nachrichten.

News

  1. Denis Fernandes da Silva is in Canada since 2022 as a postdoctoral researcher where he
    has received a scholarship funded by that country.

  2. Members of the group Eduardo Hernandez, Michelle Pierri, Denis Fernandes, José Paulo Carvalho dos Santos and Sergey Trofimchuk were invited to join the editorial board of the journals
    Fractal and Fractional https://www.mdpi.com/journal/fractalfract
    Malaya Journal of Matematik www.malayajournal.org
    Results in Nonlinear Analysis - RNA (ISSN 2636-7556) https://resultsinnonlinearanalysis.wordpress.com/
    Open Physics da Editora De Gruyter https://www.degruyter.com/journal/key/PHYS/html
    Electronic Journal of Qualitative Theory of Differential Equations http://emis.impa.br/EMIS/journals/EJQTDE/index.html

  3. Recently, Professor Eduardo Hernandez appeared on the list of the most influential scientists in the world.
    See the research conducted by Stanford University, in the United States in https://doi.org/10.1371/journal.pbio.3000918. USP reported in https://jornal.usp.br/universidade/pesquisadores-da-usp-estao-entre-os-mais-influentes-da-ciencia-mundial/