Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 2
Existence and multiplicity of positive solutions for discrete anisotropic equations
- Pages
- 297–310
- DOI
- —
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.
Özet
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.