Eigenvalues and Eigenfunctions of Discrete Conjugate Boundary Value Problems

Abstract

We consider the following boundary value problem: (−1)n−pΔny=λF(k,y,Δy,…,Δn−1y), n≪2, 0≤k≤m, Δiy(0)=0, 0≤i≤p−1; Δiy(m+n−i)=0, 0≤i≤n−p−1, where 1 ≤ p ≤ n − 1 is fixed and λ > 0. A characterization of the values of λ is carried out so that the boundary value problem has a positive solution. Next, for λ = 1, criteria are developed for the existence of two positive solutions of the boundary value problem. In addition, for particular cases we also offer upper and lower bounds for these positive solutions. Several examples are included to dwell upon the importance of the results obtained.

Department(s)

Mathematics and Statistics

Keywords and Phrases

eigenvalues; positive solutions; difference equations

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1999 Elsevier, All rights reserved.

Publication Date

01 Jan 1999

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