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

Authors:
Shugui Kang;Sui Sun Cheng
Affiliations:
College of Mathematics and Computer Science, Shanxi Datong University, Datong, Shanxi 037009, PR China;Department of Mathematics, Tsing Hua University, Hsinchu, 30043, Taiwan, ROC
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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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 @f(x)=@!"["x","x"+"@w"]"@?"@WK(x,y)f(y,@f(y-@t(y)))dy,x@?@W, is considered, where @W is a closed subset of R^N with a periodic structure. Our main result is different from most existing results since they provide three constant sign periodic solutions only.