Nontrivial solutions for a nonlinear discrete elliptic equation with periodic boundary conditions

被引：55
作者：
Bai, Liang
Zhang, Guang
机构：
[1] Qingdao Technol Univ, Sch Sci, Qingdao 266033, Peoples R China
[2] Tianjin Univ Commerce, Sch Sci, Tianjin 300134, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 210卷 / 02期
关键词：
Discrete elliptic equation; Periodic boundary condition; Mountain pass lemma; Linking theorem; Morse theory; SINH-POISSON EQUATION; POSITIVE SOLUTIONS; EXISTENCE; STABILITY; ARRAYS; SYSTEM;
D O I：
10.1016/j.amc.2008.12.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, existence of nontrivial solutions for a nonlinear discrete elliptic equation with periodic boundary conditions is considered by using the monotone operator principle, Mountain pass lemma, Linking theorem and some results in Morse theory. The obtained results are also valid and new for the corresponding difference periodic boundary value problem. (c) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：321 / 333
页数：13
相关论文
共 31 条
[1]  
[Anonymous], 1996, VARIATIONAL METHODS, DOI DOI 10.1007/978-3-662-03212-1
[2]  
[Anonymous], 1997, SPRINGER SERIES COMP
[3]  
[Anonymous], 1986, CBMS REG C SER MATH
[4]  
Cheng S. S., 2003, PARTIAL DIFFERENCE E
[5]   Doubly periodic and multiple pole solutions of the sinh-Poisson equation: Application of reciprocal transformations in subsonic gas dynamics [J].
Chow, KW ;
Mak, CC ;
Rogers, C ;
Schief, WK .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 190 (1-2) :114-126
[6]   Stability of periodic arrays of vortices [J].
Dauxois, T ;
Fauve, S ;
Tuckerman, L .
PHYSICS OF FLUIDS, 1996, 8 (02) :487-495
[7]   Delta-promoted filopodia mediate long-range lateral inhibition in Drosophila [J].
de Joussineau, C ;
Soulé, J ;
Martin, M ;
Anguille, C ;
Montcourrier, P ;
Alexandre, D .
NATURE, 2003, 426 (6966) :555-559
[8]  
Deimling K., 1985, NONLINEAR FUNCTIONAL
[9]   Solvent tuning of electrochemical potentials in the active sites of HiPIP versus ferredoxin [J].
Dey, Abhishek ;
Jenney, Francis E., Jr. ;
Adams, Michael W. W. ;
Babini, Elena ;
Takahashi, Yasuhiro ;
Fukuyama, Keiichi ;
Hodgson, Keith O. ;
Hedman, Britt ;
Solomon, Edward I. .
SCIENCE, 2007, 318 (5855) :1464-1468
[10]   Complex spatial group patterns result from different animal communication mechanisms [J].
Eftimie, R. ;
de Vries, G. ;
Lewis, M. A. .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2007, 104 (17) :6974-6979
1234