Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters
-
1472
Downloads
-
2146
Views
Authors
Yanxia Wang
- Department of Mathematics, Northwest Normal University, 730070, Lanzhou, P. R. China.
Chenghua Gao
- Department of Mathematics, Northwest Normal University, 730070, Lanzhou, P. R. China.
Tianmei Geng
- Department of Mathematics, Northwest Normal University, 730070, Lanzhou, P. R. China.
Abstract
In this paper, we consider the existence of three solutions and infinitely many solutions for discrete
fourth-order boundary value problems with multiple parameters under the different suitable hypotheses,
respectively. The approach we use is the critical point theory.
Share and Cite
ISRP Style
Yanxia Wang, Chenghua Gao, Tianmei Geng, Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3212--3225
AMA Style
Wang Yanxia, Gao Chenghua, Geng Tianmei, Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters. J. Nonlinear Sci. Appl. (2016); 9(5):3212--3225
Chicago/Turabian Style
Wang, Yanxia, Gao, Chenghua, Geng, Tianmei. "Multiplicity solutions for discrete fourth-order boundary value problem with multiple parameters." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3212--3225
Keywords
- Discrete fourth-order boundary value problem
- multiple solutions
- critical point theory
- Lipschitz condition.
MSC
References
-
[1]
D. R. Anderson, F. Minhós, A discrete fourth-order Lidstone problem with parameters, Appl. Math. Comput., 214 (2009), 523-533.
-
[2]
R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York (2000)
-
[3]
R. P. Agarwal, P. J. Y. Wong , Advanced Topics in Difference Equations, Kluwer Academic Publishers, (1997)
-
[4]
G. Bonanno, G. M. Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl., 2009 (2009), 20 pages.
-
[5]
G. Bonanno, P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), 3031-3059.
-
[6]
G. Bonanno, S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1-10.
-
[7]
X. Deng, Nonexistence and existence results for a class of fourth-order difference mixed boundary value problems, J. Appl. Math. Comput., 45 (2014), 1-14.
-
[8]
T. He, Y. Su , On discrete fourth-order boundary value problems with three parameters, J. Comput. Appl. Math., 233 (2010), 2506-2520.
-
[9]
Z. He, J. Yu, On the existence of positive solutions of fourth-order difference equations, Appl. Math. Comput., 161 (2005), 139-148.
-
[10]
J. Henderson, Positive solutions for nonlinear difference equations, Nonlinear Stud., 4 (1997), 29-36.
-
[11]
X. Liu, Y. Zhang, H. Shi, X. Deng, Periodic and subharmonic solutions for fourth-order nonlinear difference equations , Appl. Math. Comput., 236 (2014), 613-620.
-
[12]
R. Ma, C. Gao, Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem, Z. Angew. Math. Phys., 64 (2013), 493-506.
-
[13]
R. Ma, C. Gao, Y. Chang, Existence of solutions of a discrete fourth-order boundary value problem, Discrete Dyn. Nat. Soc., 2010 (2010), 19 Pages.
-
[14]
R. Ma, J. Li, C. Gao, Existence of positive solutions of a discrete elastic beam equation, Discrete Dyn. Nat. Soc., 2010 (2010), 15 Pages.
-
[15]
R. Ma, Y. Xu, Existence of positive solution for nonlinear fourth-order difference equations , Comput. Math. Appl., 59 (2010), 3770-3777.
-
[16]
M. K. Moghadam, S. Heidarkhani, J. Henderson, Infinitely many solutions for perturbed difference equations, J. Difference Equ. Appl., 20 (2014), 1055-1068.
-
[17]
B. Ricceri , A general variational principle and some of its applications, J. Comput. Appl. Math., 113 (2000), 401-410.
-
[18]
Y. Xu, C. Gao, R. Ma, Solvability of a nonlinear fourth-order discrete problem at resonance, Appl. Math. Comput., 216 (2010), 662-670.
-
[19]
B. Zhang, L. Kong, Y. Sun, X. Deng, Existence of positive solutions for BVPs of fourth-order difference equations, J. Appl. Math. Comput., 131 (2002), 583-591.