Marek GALEWSKI, Renata WIETESKA

Existence and multiplicity of positive solutions for discrete anisotropic equations

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 (a (k) |D u(k-1)|p(k-1)-2D u(k-1)) + l f(k,u(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.

Anahtar Kelimeler:

Discrete boundary value problem, variational methods, Ekeland's variational principle, mountain pass theorem, Karush--Kuhn--Tucker theorem, positive solution, anisotropic problem

Existence and multiplicity of positive solutions for discrete anisotropic equations

Keywords:

Discrete boundary value problem, variational methods, Ekeland's variational principle, mountain pass theorem, Karush--Kuhn--Tucker theorem, positive solution, anisotropic problem,

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