Original scientific paper

**Measure pseudo affine-periodic solutions of semilinear differential equations**

Zhinan Xia
; Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, China

Zihui Li
; Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, China

Dingjiang Wang
; Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, China

###### Abstract

n 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.

###### Keywords

Measure pseudo affine-periodic function, measure theory, exponential dichotomy, Banach contraction mapping principle, Leray-Schauder alternative theorem

###### Hrčak ID:

198693

###### URI

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