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
  • [1] Existence and multiplicity results for discrete anisotropic equations
    Ouhamou, Brahim
    Ayoujil, Abdesslem
    Berrajaa, Mohammed
    Journal of Nonlinear Functional Analysis, 2021, 2021
  • [2] EXISTENCE AND MULTIPLICITY RESULTS FOR DISCRETE ANISOTROPIC EQUATIONS
    Ouhamou, Brahim
    Ayoujil, Abdesslem
    Berrajaa, Mohammed
    JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2021,
  • [3] Existence and Multiplicity of Solutions for Anisotropic Elliptic Equations
    El Amrouss, Abdelrachid
    El Mahraoui, Ali
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2022, 40
  • [4] Positive Solutions for Biharmonic Equations: Existence, Uniqueness and Multiplicity
    Meiqiang Feng
    Mediterranean Journal of Mathematics, 2023, 20
  • [5] Positive Solutions for Biharmonic Equations: Existence, Uniqueness and Multiplicity
    Feng, Meiqiang
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (06)
  • [6] Existence and multiplicity of solutions for anisotropic elliptic equations with variable exponent
    El Amrouss, Abdelrachid
    El Mahraoui, Ali
    ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2020, 47 (02): : 252 - 266
  • [7] GLOBAL EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR ANISOTROPIC EIGENVALUE PROBLEMS
    Liu, Zhenhai
    Papageorgiou, Nikolaos S.
    MATHEMATICA SLOVACA, 2024, 74 (03) : 679 - 690
  • [8] EXISTENCE OF POSITIVE SOLUTIONS OF DISCRETE DELAYED EQUATIONS
    Bastinec, Jaromir
    Diblik, Josef
    APLIMAT 2007 - 6TH INTERNATIONAL CONFERENCE, PT II, 2007, : 143 - 148
  • [9] Existence, Localization and Multiplicity of Positive Solutions to φ-Laplace Equations and Systems
    Herlea, Diana-Raluca
    Precup, Radu
    TAIWANESE JOURNAL OF MATHEMATICS, 2016, 20 (01): : 77 - 89
  • [10] MULTIPLICITY RESULTS FOR DISCRETE ANISOTROPIC EQUATIONS
    Galewski, Marek
    Heidarkhani, Shapour
    Salari, Amjad
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (01): : 203 - 218
12345