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Volume 8
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10.3390/math8112030
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Article

Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian

by
Sijia Du
1,2 and
Zhan Zhou
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.
Mathematics 2020, 8(11), 2030; https://doi.org/10.3390/math8112030
Submission received: 18 October 2020 / Revised: 7 November 2020 / Accepted: 12 November 2020 / Published: 14 November 2020
(This article belongs to the Special Issue Advances in Nonlinear Spectral Theory)
Versions Notes

Abstract

Due to the applications in many fields, there is great interest in studying partial difference equations involving functions with two or more discrete variables. In this paper, we deal with the existence of infinitely many solutions for a partial discrete Dirichlet boundary value problem with the p-Laplacian by using critical point theory. Moreover, under appropriate assumptions on the nonlinear term, we determine open intervals of the parameter such that at least two positive solutions and an unbounded sequence of positive solutions are obtained by using the maximum principle. We also show two examples to illustrate our results.
Keywords: partial difference equations; boundary value problem; p-laplacian; multiple solutions; critical point theory partial difference equations; boundary value problem; p-laplacian; multiple solutions; critical point theory

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MDPI and ACS Style

Du, S.; Zhou, Z. Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian. Mathematics 2020, 8, 2030. https://doi.org/10.3390/math8112030

AMA Style

Du S, Zhou Z. Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian. Mathematics. 2020; 8(11):2030. https://doi.org/10.3390/math8112030

Chicago/Turabian Style

Du, Sijia, and Zhan Zhou. 2020. "Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian" Mathematics 8, no. 11: 2030. https://doi.org/10.3390/math8112030

APA Style

Du, S., & Zhou, Z. (2020). Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian. Mathematics, 8(11), 2030. https://doi.org/10.3390/math8112030

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