ASYMPTOTIC NONUNIFORM NONRESONANCE CONDITIONS FOR A NONLINEAR DISCRETE BOUNDARY VALUE PROBLEM

TitleASYMPTOTIC NONUNIFORM NONRESONANCE CONDITIONS FOR A NONLINEAR DISCRETE BOUNDARY VALUE PROBLEM
Publication TypeJournal Article
Year of Publication2008
AuthorsMA RUYUN, O’REGAN DONAL
JournalDynamic Systems and Applications
Volume17
Start Page271
Pagination11
Date Published2008
ISSN1056-2176
AMS Subject Classification39A10
Abstract

Let T := {a+1, . . . , b+1}. We study the solvability of nonlinear discrete two-point boundary value problem ( ∆2u(t − 1) + g(t, u(t)) = h(t), t ∈ T, u(a) = u(b + 2) = 0 where h : T → R, g : T × R → R satisfies α(t) ≤ lim inf |x|→∞ x −1 g(t, x) ≤ lim sup |x|→∞ x −1 g(t, x) ≤ β(t) uniformly on T, and α and β satisfy some nonresonance conditions of nonuniform type with respect to two consecutive eigenvalues of the associated linear problem. The proof is based on the LeraySchauder continuation theorem.

PDFhttps://acadsol.eu/dsa/articles/17/DSA-2007-271-282.pdf
Refereed DesignationRefereed