Existence and regularity of solutions for non-autonomous integrodifferential evolution equations involving nonlocal conditions

Abstract

In this article, we investigate the existence and regularity of solutions for non-autonomous integrodifferential evolution equations involving nonlocal conditions. Using the theory of resolvent operators, some fixed point theorems, and an estimation technique of Kuratowski measure of noncompactness, we first establish some existence results of mild solutions for the proposed equation. Subsequently, we show by applying a newly established lemma that these solutions have regularity property under some conditions. Finally, as a sample of application, the obtained results are applied to a class of non-autonomous nonlocal partial integrodifferential equations.

Keywords

• non-autonomous integrodifferential evolution equation
• resolvent operator
• fixed point theorem
• nonlocal condition
• 34k30
• 37b55
• 45n05
• 47n20
• 49n60