Measure pseudo affine-periodic solutions of semilinear differential equations

Abstract

In this paper, we introduce the concept of pseudo affine-periodic functionvia measure theory, that is measure pseudo $(Q, T)$-affine-periodic function.Existence, uniqueness of measure pseudo $(Q, T)$-affine-periodic solutionfor semilinear  differential equations are investigated.The working tools are based on the  Banach contraction mapping principleand Leray-Schauder alternative theorem.Finally, an example is presented to illustrate the main findings.