Neutral multivalued integro-differential evolution equations with infinite state-dependent delay

2020 ◽  
Vol 44 (6) ◽  
pp. 2312-2329
Author(s):  
Abdelaziz MEBARKI ◽  
Selma BAGHLI-BENDIMERAD
Keyword(s):  
Differential Evolution ◽  
Evolution Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Infinite State

scholarly journals A Note on Existence of Mild Solutions for Second-Order Neutral Integro-Differential Evolution Equations with State-Dependent Delay

2021 ◽  
Vol 5 (3) ◽  
pp. 126
Author(s):  
Shahram Rezapour ◽  
Hernán R. Henríquez ◽  
Velusamy Vijayakumar ◽  
Kottakkaran Sooppy Nisar ◽  
Anurag Shukla
Keyword(s):  
Differential Evolution ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Second Order ◽  
State Dependent ◽  
Retarded Functional Differential Equations ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Infinite State

This article is mainly devoted to the study of the existence of solutions for second-order abstract non-autonomous integro-differential evolution equations with infinite state-dependent delay. In the first part, we are concerned with second-order abstract non-autonomous integro-differential retarded functional differential equations with infinite state-dependent delay. In the second part, we extend our results to study the second-order abstract neutral integro-differential evolution equations with state-dependent delay. Our results are established using properties of the resolvent operator corresponding to the second-order abstract non-autonomous integro-differential equation and fixed point theorems. Finally, an application is presented to illustrate the theory obtained.

scholarly journals Existence results for fractional integro-differential inclusions with state-dependent delay

2017 ◽  
Vol 4 (1) ◽  
pp. 62-77
Author(s):  
Giovana Siracusa ◽  
Hernán R. Henríquez ◽  
Claudio Cuevas
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Existence Results ◽  
Materials With Memory ◽  
State Dependent ◽  
State Dependent Delay ◽  
Contractive Maps ◽  
Infinite State ◽  
With Memory ◽  
Condensing Maps

AbstractIn this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

scholarly journals Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Abdessalam Baliki ◽  
Mouffak Benchohra
Keyword(s):  
Banach Space ◽  
Global Existence ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Functional Evolution ◽  
State Dependent ◽  
State Dependent Delay ◽  
Existence And Stability ◽  
Semilinear Evolution Equations

AbstractIn this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.

Sign in / Sign up

Export Citation Format

Share Document