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

Johnny Henderson and Susan D. Lauer

Abstract and Applied Analysis, 1997, vol. 2, 1-9

Abstract:

The n th order eigenvalue problem: Δ n x ( t ) = ( − 1 ) n − k λ f ( 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 f 0 ( t ) = lim n → 0 + f ( t , u ) u and f ∞ ( t ) = lim n → ∞ 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:696821

DOI: 10.1155/S1085337597000390

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