Large Constant-Sign Solutions of Discrete Dirichlet Boundary Value Problems with <i>p</i>-Mean Curvature Operator

Abstract

In this paper, we consider the existence of infinitely many large constant-sign solutions for a discrete Dirichlet boundary value problem involving p -mean curvature operator. The methods are based on the critical point theory and truncation techniques. Our results are obtained by requiring appropriate oscillating behaviors of the non-linear term at infinity, without any symmetry assumptions.

Keywords

• discrete dirichlet boundary value problem
• <i>p</i>-mean curvature operator
• constant-sign solutions
• discrete maximum principle
• critical point theory