Existence of three solutions for difference equations through variational methods

Document Type : Original Paper


Department of Mathematics, Razi University, Kermanshah, Iran


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.


Main Subjects

1. Atici, F. M. and Cabada, A. (2003). Existence and uniqueness results for
discrete second-order periodic boundary value problems, Comput. Math.
Appl. 45, 1417-1427.
2.Atici, F. M. and Guseinov, G. S. (1999). Positive periodic solutions for
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-
4. Bonanno, G. and Candito, P. (2009). Nonlinear difference equations
investigated via critical point methods, Nonlinear Anal. TMA 70, 3180-
5.Cabada, A., Iannizzotto, A. and Tersian, S. (2009). Multiple solutions for
discrete boundary value problem, J. Math. Anal. Appl. 356, 418-428. 
Volume 10, Issue 2
December 2020
Pages 400-417
  • Receive Date: 06 August 2019
  • Revise Date: 28 May 2020
  • Accept Date: 23 June 2020
  • First Publish Date: 21 December 2020