Electron. J. Differential Equations, Vol. 2020 (2020), No. 115, pp. 1-12.

Existence and multiplicity of homoclinic solutions for a difference equation

Shapour Heidarkhani, Fariba Gharehgazlouei, Maurizio Imbesi

Abstract:
The aim of this article is to obtain homoclinic solutions for a discrete problem involving p-Laplacian. We prove the existence of at least one, two and three solutions for the problem. Our approach is based on variational methods.

Submitted January 14, 2020. Published November 23, 2020.
Math Subject Classifications: 39A10, 47J30, 35B38.
Key Words: Difference equations; discrete p-Laplacian; variational methods.
DOI: 10.58997/ejde.2020.115

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Shapour Heidarkhani
Department of Mathematics
Faculty of Sciences
Razi University
67149 Kermanshah, Iran
email: s.heidarkhani@razi.ac.ir
Fariba Gharehgazlouei
Department of Mathematics
Faculty of Sciences
Razi University
67149 Kermanshah, Iran
email: f.gharehgazloo@yahoo.com
  Maurizio Imbesi
Department of Mathematical and Computer Sciences
Physical and Earth Sciences
University of Messina
Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
email: imbesim@unime.it

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