Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Existence of three solutions for difference equations through variational methods

Document Type : Original Paper

Authors
Shapour Heidarkhani
Amjad Salari
Department of Mathematics, Razi University, Kermanshah, Iran
10.22055/jamm.2020.30573.1746
Abstract
This paper is devoted to the study of the multiplicity results of solutions for a class of difference equations. Indeed, we will use variational methods for smooth functionals, defined on the reflexive Banach spaces in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are non-negative, we will prove that the solutions are non-negative. Finally, by presenting one example, we will ensure the applicability of our results.
Keywords
Three solutions
Nonlinear difference equations
Discrete boundary value problem
Lipschitz condition
Variational methods
Critical point theory
Subjects
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nonlinear difference equations with J. periodic coefficients, Math. Anal.
Appl. 232, 166-182.
3.Bonanno, G. and Candito, P. (2009). Infinitely many solutions for a class
of discrete non-linear boundary value problems, Appl. Anal. 884, 605-
616.
4. Bonanno, G. and Candito, P. (2009). Nonlinear difference equations
investigated via critical point methods, Nonlinear Anal. TMA 70, 3180-
3186.
5.Cabada, A., Iannizzotto, A. and Tersian, S. (2009). Multiple solutions for
discrete boundary value problem, J. Math. Anal. Appl. 356, 418-428. 
Journal of Advanced Mathematical Modeling
Volume 10, Issue 2
December 2020
Pages 400-417

  • Receive Date 06 August 2019
  • Revise Date 28 May 2020
  • Accept Date 23 June 2020