Existence and multiplicity of positive solutions for discrete anisotropic equations

Authors : Marek GALEWSKI, Renata WIETESKA

Pages : 297-310

Doi:10.3906/mat-1303-6

View : 13 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function a , a nonlinear term f, and a numerical parameter l :D insert ignore into journalissuearticles values(a insert ignore into journalissuearticles values(k); |D uinsert ignore into journalissuearticles values(k-1);|pinsert ignore into journalissuearticles values(k-1);-2D uinsert ignore into journalissuearticles values(k-1);); + l finsert ignore into journalissuearticles values(k,uinsert ignore into journalissuearticles values(k););=0, k\in [1,T] . We derive the intervals of a numerical parameter l for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.
Keywords : Discrete boundary value problem, variational methods, Ekeland`s variational principle, mountain pass theorem, Karush Kuhn Tucker theorem, positive solution, anisotropic problem