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Article

Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator

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.
Academic Editor: Jan Awrejcewicz
Symmetry 2021, 13(7), 1207; https://doi.org/10.3390/sym13071207
Received: 25 May 2021 / Revised: 30 June 2021 / Accepted: 3 July 2021 / Published: 5 July 2021
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example. View Full-Text
Keywords: boundary value problem; partial difference equation; infinitely many small solutions; (p,q)-Laplacian; critical point theory boundary value problem; partial difference equation; infinitely many small solutions; (p,q)-Laplacian; critical point theory
MDPI and ACS Style

Xiong, F.; Zhou, Z. Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator. Symmetry 2021, 13, 1207. https://doi.org/10.3390/sym13071207

AMA Style

Xiong F, Zhou Z. Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator. Symmetry. 2021; 13(7):1207. https://doi.org/10.3390/sym13071207

Chicago/Turabian Style

Xiong, Feng, and Zhan Zhou. 2021. "Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator" Symmetry 13, no. 7: 1207. https://doi.org/10.3390/sym13071207

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