Existence and uniqueness of solutions, well-posedness and global attractor for abstract differential equations with state-dependent delay

2021 ◽  
Vol 302 ◽  
pp. 753-806
Author(s):  
Eduardo Hernandez ◽  
Denis Fernandes ◽  
Jianhong Wu
Keyword(s):  
Differential Equations ◽  
Global Attractor ◽  
Existence And Uniqueness ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay

-ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY

2018 ◽  
Vol 98 (3) ◽  
pp. 456-464 ◽  
Author(s):  
EDUARDO HERNÁNDEZ ◽  
MICHELLE PIERRI
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Periodic Solutions ◽  
General Class ◽  
Existence And Uniqueness ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Asymptotically Periodic ◽  
Asymptotically Periodic Solutions

We study the existence and uniqueness of${\mathcal{S}}$-asymptotically periodic solutions for a general class of abstract differential equations with state-dependent delay. Some examples related to problems arising in population dynamics are presented.

Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

2019 ◽  
Vol 62 (3) ◽  
pp. 771-788 ◽  
Author(s):  
Eduardo Hernández ◽  
Jianhong Wu
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Solutions ◽  
Almost Periodic ◽  
Qualitative Properties ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Asymptotically Almost Periodic

AbstractWe study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.

Well-posedness of Stratonovich multi-valued SDEs driven by semimartingales

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005
Author(s):  
Jing Wu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Change ◽  
Random Time ◽  
Approximation Technique ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Random Time Change

In this paper we consider Stratonovich type multi-valued stochastic differential equations (MSDEs) driven by general semimartingales. Based on an existence and uniqueness result for MSDEs with respect to continuous semimartingales, we apply the random time change and approximation technique to prove existence and uniqueness of solutions to Stratonovich type multi-valued SDEs driven by general semimartingales with summable jumps.

Wellposedness of abstract differential equations with state-dependent delay

2018 ◽  
Vol 291 (13) ◽  
pp. 2045-2056
Author(s):  
Eduardo Hernández ◽  
Katia A. G. Azevedo ◽  
Vanessa Rolnik
Keyword(s):  
Differential Equations ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay

scholarly journals Global Attractor for Partial Functional Differential Equations with State-Dependent Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhimin He ◽  
Bo Du
Keyword(s):  
Differential Equations ◽  
Global Attractor ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Global Attractors ◽  
Partial Functional Differential Equations ◽  
State Dependent ◽  
Classic Theory ◽  
State Dependent Delay ◽  
Functional Differential

This work aims to investigate the existence of global attractors for a class of partial functional differential equations with state-dependent delay. Using the classic theory about global attractors in infinite dimensional dynamical systems, we obtain some sufficient conditions for guaranteeing the existence of a global attractor.

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