Existence of homoclinic solutions for a nonlinear fourth order $ p $-Laplacian difference equation

Nikolay Dimitrov; Stepan Tersian

doi:10.3934/dcdsb.2019254

Article Contents

2020, Volume 25, Issue 2: 555-567. Doi: 10.3934/dcdsb.2019254

This issue Previous Article Nonnegative oscillations for a class of differential equations without uniqueness: A variational approach Next Article Well-posedness results for fractional semi-linear wave equations

Existence of homoclinic solutions for a nonlinear fourth order $ p $-Laplacian difference equation

Nikolay Dimitrov^1, , and
Stepan Tersian^2,

1.
Department of Mathematics, University of Ruse, 7017 Ruse, Bulgaria
2.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

^* Corresponding author: Nikolay Dimitrov
^* Corresponding author: Nikolay Dimitrov

Received: August 31, 2018

Revised: October 31, 2018

Early access: November 2019

Published: February 2020

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Abstract

The aim of this paper is the study of existence of homoclinic solutions for a nonlinear difference equation involving $ p $-Laplacian. Under suitable growth conditions we prove that the considered problem has at least one homoclinic solution. The proof is based on the mountain-pass theorem with Cerami's condition, Brezis-Lieb lemma and variational method.

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Mathematics Subject Classification: Primary: 34B15, 34C37; Secondary: 39A10.

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References

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