- Turkish Journal of Mathematics
- Vol: 38 Issue: 2
- Existence and multiplicity of positive solutions for discrete anisotropic equations
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 : 14 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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 (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.Keywords : Discrete boundary value problem, variational methods, Ekeland's variational principle, mountain pass theorem, Karush--Kuhn--Tucker theorem, positive solution, anisotropic problem