Existence of solutions for delay evolution equations with nonlocal conditions

Abstract

In this paper, we are devoted to study the existence of mild solutions for delay evolution equations with nonlocal conditions. By using tools involving the Kuratowski measure of noncompactness and fixed point theory, we establish some existence results of mild solutions without the assumption of compactness on the associated semigroup. Our results improve and generalize some related conclusions on this issue. Moreover, we present an example to illustrate the application of the main results.

Keywords

• evolution equation
• nonlocal conditions
• delay
• mild solution
• kuratowski measure of noncompactness
• equicontinuous semigroup
• 34g20
• 34k30
• 35d35