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.
引用
收藏
页码：297 / 310
页数：14
相关论文
共 50 条
  • [31] Existence and multiplicity of positive periodic solutions to a class of Lienard equations with repulsive singularities
    Wang, Jinrong
    Wang, Ben
    Miao, Yongwei
    Yu, Xingchen
    JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2022, 24 (03)
  • [32] Existence and multiplicity of positive solutions for fractional q-difference equations with parameter
    Li, Xinhui
    Han, Zhenlai
    Zhao, Yan
    INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2015, 5 (04) : 267 - 287
  • [33] Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects
    Li, XY
    Lin, XN
    Jiang, DQ
    Zhang, XY
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (04) : 683 - 701
  • [34] Existence and multiplicity of positive periodic solutions to functional differential equations with infinite delay
    School of Sciences, Northeastern University, Shenyang 110004, China
    不详
    Dongbei Daxue Xuebao, 2007, 5 (757-760):
  • [35] Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations
    Agarwal, RP
    Cao, DM
    Lü, HS
    O'Regan, D
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2006, 58 (03): : 449 - 475
  • [36] EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR A SYSTEM OF DIFFERENCE EQUATIONS WITH COUPLED BOUNDARY CONDITIONS
    Henderson, Johnny
    Luca, Rodica
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2017, 7 (01): : 134 - 146
  • [37] Existence and multiplicity of positive solutions for a class of p ( x )-Kirchhoff type equations
    Ma, Ruyun
    Dai, Guowei
    Gao, Chenghua
    BOUNDARY VALUE PROBLEMS, 2012, : 1 - 16
  • [38] Existence and multiplicity of positive solutions for a class of p(x)-Kirchhoff type equations
    Ruyun Ma
    Guowei Dai
    Chenghua Gao
    Boundary Value Problems, 2012
  • [39] An Existence Result for Discrete Anisotropic Equations
    Heidarkhani, Shapour
    Afrouzi, Ghasem A.
    Moradi, Shahin
    TAIWANESE JOURNAL OF MATHEMATICS, 2018, 22 (03): : 725 - 739
  • [40] EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR DISCRETE INCLUSIONS
    Marcu, Nicu
    Bisci, Giovanni Molica
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
12345