Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations. (1997)

• Record Type: Journal Article
• Authors: Henderson, Johnny; Lauer, Susan D.
• Is Part Of: Abstract and applied analysis. Volume 2:Number 3/4(1997)
• Page Start: 271
• Page End: 279
• Publication Date: 1997
• Subjects: nth order difference equation -- eigenvalue -- boundary value problem -- fixed point theorem -- discrete -- nonlinear -- Green's function; Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337597000390
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Then 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, wheren ≥ 2 andk ∈ { 1, 2, …, n − 1 } are given. Eigenvaluesλ are determined forf continuous and the case where the limitsf 0 ( t ) = lim n → 0 + f ( t, u ) u andf ∞ ( t ) = lim n → ∞ f ( t, u ) u exist for allt ∈ [ 0, T ] . Guo's fixed point theorem is applied to operators defined on annular regions in a cone.