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

by Jianxia Wang 1,2 and Zhan Zhou 1,2,*
1
School of Mathematics and Information Science, Guangzhou University, Guangdong 510006, China
2
Center for Applied Mathematics, Guangzhou University, Guangdong 510006, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 381; https://doi.org/10.3390/math8030381
Received: 3 February 2020 / Revised: 4 March 2020 / Accepted: 5 March 2020 / Published: 9 March 2020
(This article belongs to the Special Issue Advances in Nonlinear Spectral Theory)
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. View Full-Text
Keywords: discrete Dirichlet boundary value problem; p-mean curvature operator; constant-sign solutions; discrete maximum principle; critical point theory discrete Dirichlet boundary value problem; p-mean curvature operator; constant-sign solutions; discrete maximum principle; critical point theory
MDPI and ACS Style

Wang, J.; Zhou, Z. Large Constant-Sign Solutions of Discrete Dirichlet Boundary Value Problems with p-Mean Curvature Operator. Mathematics 2020, 8, 381.

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