Turkish Journal of Mathematics
Abstract
In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function \alpha , a nonlinear term f, and a numerical parameter \lambda :\Delta (\alpha (k) \Delta u(k-1) ^{p(k-1)-2}\Delta u(k-1)) + \lambda f(k,u(k))=0, k\in [1,T] . We derive the intervals of a numerical parameter \lambda for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.
DOI
10.3906/mat-1303-6
Keywords
Discrete boundary value problem, variational methods, Ekeland's variational principle, mountain pass theorem, Karush--Kuhn--Tucker theorem, positive solution, anisotropic problem
First Page
297
Last Page
310
Recommended Citation
GALEWSKI, M, & WIETESKA, R (2014). Existence and multiplicity of positive solutions for discrete anisotropic equations. Turkish Journal of Mathematics 38 (2): 297-310. https://doi.org/10.3906/mat-1303-6
