The Existence and Multiplicity of Homoclinic Solutions for a Fractional Discrete p−Laplacian Equation
Mathematics, Volume 10, No. 9, Article 1400, Year 2022
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In this study, we investigate the existence and multiplicity of solutions for a fractional discrete p−Laplacian equation on Z. Under suitable hypotheses on the potential function V and the nonlinearity f, with the aid of Ekeland’s variational principle, via mountain pass lemma, we obtain that this equation exists at least two nonnegative and nontrivial homoclinic solutions when the real parameter λ > 0 is large enough.