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

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

In this paper, we consider the existence of infinitely many large constant-sign solutions for a discrete Dirichlet boundary value problem involving <inline-formula> <math display="inline"> <semantics> <mi mathvariant="italic">p</mi> </semantics>...

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Bibliographic Details
Main Authors: Jianxia Wang, Zhan Zhou
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Mathematics
Subjects:
discrete dirichlet boundary value problem
<i>p</i>-mean curvature operator
constant-sign solutions
discrete maximum principle
critical point theory
Online Access:https://www.mdpi.com/2227-7390/8/3/381
Description
Summary:In this paper, we consider the existence of infinitely many large constant-sign solutions for a discrete Dirichlet boundary value problem involving <inline-formula> <math display="inline"> <semantics> <mi mathvariant="italic">p</mi> </semantics> </math> </inline-formula>-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.
ISSN:2227-7390

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