Ground state sign-changing homoclinic solutions for a discrete nonlinear p-Laplacian equation with logarithmic nonlinearity

2023/11/15 by Xin Ou, Xingyong Zhang, Ou, Xin +1
Mathematics · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2311.08777

Abstract

By using a direct non-Nehari manifold method from [X.H. Tang, B.T. Cheng. J. Differ. Equations. 261(2016), 2384-2402.], we obtain an existence result of ground state sign-changing homoclinic solution which only changes sign one times and ground state homoclinic solution for a class of discrete nonlinear p-Laplacian equation with logarithmic nonlinearity. Moreover, we prove that the sign-changing ground state energy is larger than twice of the ground state energy.

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