Abstract
The aim of this paper is the study of existence of solutions for nonlinear $2n^{\rm th}$-order difference equations involving $p$-Laplacian. In the first part, the existence of a nontrivial homoclinic solution for a discrete $p$-Laplacian problem is proved. The proof is based on the mountain-pass theorem of Brezis and Nirenberg. Then, we study the existence of multiple solutions for a discrete $p$-Laplacian boundary value problem. In this case the proof is based on the three critical points theorem of Averna and Bonanno.
Citation
Lorena Saavedra. Stepan Tersian. "Existence of solutions for nonlinear $p$-Laplacian difference equations." Topol. Methods Nonlinear Anal. 50 (1) 151 - 167, 2017. https://doi.org/10.12775/TMNA.2017.022
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