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Article

Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with ϕc-Laplacian

by 1,2 and 1,2,*
1
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
2
Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(11), 1839; https://doi.org/10.3390/sym12111839
Received: 14 October 2020 / Revised: 1 November 2020 / Accepted: 3 November 2020 / Published: 6 November 2020
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating behavior at infinity on the nonlinear term f, we respectively obtain the sufficient conditions for the existence of at least three non-trivial solutions and the existence of at least two non-trivial solutions under different assumptions on f. In addition, by using the maximum principle, we also deduce the existence of at least three positive solutions from our conclusion. As far as we know, our results are supplements to some well-known ones. View Full-Text
Keywords: ϕc-Laplacian; boundary value problem; critical point theory; three solutions ϕc-Laplacian; boundary value problem; critical point theory; three solutions
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MDPI and ACS Style

Chen, Y.; Zhou, Z. Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with ϕc-Laplacian. Symmetry 2020, 12, 1839. https://doi.org/10.3390/sym12111839

AMA Style

Chen Y, Zhou Z. Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with ϕc-Laplacian. Symmetry. 2020; 12(11):1839. https://doi.org/10.3390/sym12111839

Chicago/Turabian Style

Chen, Yanshan, and Zhan Zhou. 2020. "Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with ϕc-Laplacian" Symmetry 12, no. 11: 1839. https://doi.org/10.3390/sym12111839

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