Abstract
We study the existence of S-asymptotically ω-periodic solutions for a class of abstract partial integro-differential equations and for a class of abstract partial integrodifferential equations with delay. Applications to integral equations arising in the study of heat conduction in materials with memory are shown.
Highlights
In this paper we study the existence of S-asymptotically ω-periodic solutions for a class of abstract integrodifferential equations of the form t u t Au tB t − s u s ds g t, u t, t ≥ 0, 1.1 u 0 x0, 1.2 where A : D A ⊆ X → X and B t : D B t ⊆ X → X for t ≥ 0 are densely defined closed linear operators in a Banach space X, ·
We study the existence of S-asymptotically ω-periodic solutions for a class of abstract partial integro-differential equations and for a class of abstract partial integrodifferential equations with delay
We assume that D A ⊂ D B t for every t ≥ 0 and that g : 0, ∞ × X → X is a suitable function
Summary
B t − s u s ds g t, u t , t ≥ 0, 1.1 u 0 x0, 1.2 where A : D A ⊆ X → X and B t : D B t ⊆ X → X for t ≥ 0 are densely defined closed linear operators in a Banach space X, ·. To the best of our knowledge, the study of the existence of S-asymptotically ω-periodic solutions for equations of type 1.1 is a topic not yet considered in the literature. To fill this gap is the main motivation of this paper. We consider some definitions, technical aspects and basic properties related with S-asymptotically ω-periodic functions and resolvent operators. As an application of our abstract results, in the fourth section, we establish conditions for the existence of S-asymptotically ω-periodic mild solutions of a specific integral equation arising in the study of heat conduction in materials with memory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
