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

Abstract

Abstract By using a direct non-Nehari manifold method from (Tang and Cheng in J. Differ. Equ. 261:2384–2402, 2016), we obtain an existence result of ground-state sign-changing homoclinic solutions that only changes sign once and ground-state homoclinic solutions for a class of discrete nonlinear p-Laplacian equations with logarithmic nonlinearity. Moreover, we prove that the sign-changing ground-state energy is larger than twice the ground-state energy.

Keywords

• Discrete p-Laplacian equations
• Ground-state sign-changing homoclinic solutions
• Ground-state homoclinic solutions
• Non-Nehari manifold
• Logarithmic nonlinearity