Turkish Journal of Mathematics
DOI
10.3906/mat-1303-6
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.
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, MAREK and WIETESKA, RENATA
(2014)
"Existence and multiplicity of positive solutions for discrete anisotropic equations,"
Turkish Journal of Mathematics: Vol. 38:
No.
2, Article 11.
https://doi.org/10.3906/mat-1303-6
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss2/11
