Existence of positive, negative and sign-changing periodic solutions for a class of integral equations

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Abstract

In this paper, the simultaneous existence of positive, negative and sign-changing periodic solutions for a class of integral equations of the form ϕ(x)=[x,x+ω]ΩK(x,y)f(y,ϕ(yτ(y)))dy,xΩ, is considered, where Ω is a closed subset of RN with a periodic structure. Our main result is different from most existing results since they provide three constant sign periodic solutions only.

MSC

34B15

Keywords

Integral equations
Cone
e-continuous
Sign-changing periodic solution
Fixed point theorem

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Project supported by the Natural Science Foundation of Shanxi Province (2008011002-1) and Shanxi Datong University and by the Development Foundation of Higher Education Department of Shanxi Province and by the Science and Technology Bureau of Datong City.