Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations

Johnny Henderson and Susan D. Lauer

Abstract and Applied Analysis, 1997, vol. 2, issue 3-4, 271-279

Abstract: The nth order eigenvalue problem: Δnx(t)=(−1) n−kλf(t,x(t)), t∈[0,T],x(0)=x(1)=⋯=x(k−1)=x(T+k+1)=⋯=x(T+n)=0, is considered, where n ≥ 2 and k ∈ {1, 2, …, n − 1} are given. Eigenvalues λ are determined for f continuous and the case where the limits f0(t)=limn→0+f(t,u)u and f∞(t)=limn→∞f(t,u)u exist for all t ∈ [0, T]. Guo′s fixed point theorem is applied to operators defined on annular regions in a cone.

Date: 1997
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https://doi.org/10.1155/S1085337597000390

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2:y:1997:i:3-4:p:271-279

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