Existence and multiplicity of positive solutions for discrete anisotropic equations

被引：22
|
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.
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页码：297 / 310
页数：14
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