Existence and multiplicity of solutions for nonlinear second order difference boundary value problems

Authors:
Xiumei He;Xian Wu
Affiliations:
Department of Mathematics, Kunming University, Kunming, Yunnan 650031, PR China;Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650092, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In the present paper, the following nonlinear second order difference boundary value problems @D[p(n-1)@Du(n-1)]+q(n)u(n)+f(n,u(n))=0,n@?Z(1,N),u(0)=u(N),p(0)@Du(0)=p(N)@Du(N) are studied by using the critical theory, and three new multiple results of solutions are obtained, where Z(1,N)={1,2,...,N},f:Z(1,N)xR-R is a continuous function in the second variable, p,q:Z(0,N)-R and p(n)0.