Classical solutions for discrete potential boundary value problems with generalized Leray-Lions type operator and variable exponent

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Résumé

In this article, we prove the existence of solutions for some discrete nonlinear difference equations subjected to a potential boundary type condition. We use a variational technique that relies on Szulkin’s critical point theory, which ensures the existence of solutions by ground state and mountain pass methods

Mots-clés

potential boundary type condition; variational method; critical point; ground state method; Palais-Smale condition; mountain pass theorem