Existence and Uniqueness of Solution for Abstract Differential Equations with State-Dependent Time Impulses

2019 ◽  
Vol 16 (2) ◽  
Author(s):  
Katia A. G. Azevedo
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Abstract Differential Equations ◽  
State Dependent

-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.

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