Existence of solutions for nonlinear p-Laplacian difference equations
Keywords
$p$-Laplacian, difference equations, mountain-pass theoremAbstract
The aim of this paper is the study of existence of solutions for nonlinear $2n^{\mathrm{th}}$-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.Published
2017-07-07
How to Cite
1.
SAAVEDRA, Lorena and TERSIAN, Stepan. Existence of solutions for nonlinear p-Laplacian difference equations. Topological Methods in Nonlinear Analysis. Online. 7 July 2017. Vol. 50, no. 1, pp. 151 - 167. [Accessed 29 March 2024].
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