Existence and multiplicity of positive solutions for discrete anisotropic equations

被引：24

作者：

Galewski, Marek ^{[1
]}

Wieteska, Renata ^{[1
]}

机构：

[1] Tech Univ Lodz, Inst Math, PL-90924 Lodz, Poland

来源：

TURKISH JOURNAL OF MATHEMATICS | 2014年 / 38卷 / 02期

关键词：

Discrete boundary value problem; variational methods; Ekeland's variational principle; mountain pass theorem; Karush-Kuhn-Tucker theorem; positive solution; anisotropic problem; BOUNDARY-VALUE-PROBLEMS; SYSTEM;

D O I：

10.3906/mat-1303-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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)vertical bar Delta u(k - 1)vertical bar(p(k-1)-2)Delta u(k - 1)) + lambda f (k, u(k)) = 0, k is an element of [1, T]. We derive the intervals of a numerical parameter A for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.

引用

页码：297 / 310

页数：14

共 23 条

[1] Multiple positive solutions of singular discrete p-Laplacian problems via variational methods [J].