    January  2018, 23(1): 487-492. doi: 10.3934/dcdsb.2018033

## On homoclinic solutions for a second order difference equation with p-Laplacian

 Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Poland

Received  July 2016 Revised  September 2016 Published  January 2018

In this paper, we obtain conditions under which the difference equation
 $-Δ ≤ft( a(k)φ _{p}(Δ u(k-1))) +b(k)φ_{p}(u(k))=λ f(k, u(k)), \;\;k∈\mathbb{Z},$
has infinitely many homoclinic solutions. A variant of the fountain theorem is utilized in the proof of our theorem. Some known results in the literature are extended and complemented.
Citation: Robert Stegliński. On homoclinic solutions for a second order difference equation with p-Laplacian. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 487-492. doi: 10.3934/dcdsb.2018033
##### References:
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##### References:
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