Mild solution in the α-norm for some partial integrodifferential equations involving a nonlocal condition

Abstract

In this work, we investigate the existence of mild solutions in the α\alpha -norm for a class of nonlocal integrodifferential equations. We employ the theory of resolvent operators introduced by R. Grimmer. The Leray-Schauder alternative is the principal working tool for our analysis.

Keywords

• mild solution
• nonlocal condition
• integrodifferential equation
• α-norm
• resolvent operator
• 45k05
• 47h10
• 47d06