Classical solutions for discrete potential boundary value problems with generalized leray-lions type operator and variable exponent
Electronic Journal of Differential Equations, Volume 2017, Article 109, Year 2017
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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.