Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator
Abstract In this paper, we prove the existence of three solutions to a partial difference equation with ( p , q ) $(p,q)$ -Laplacian operator by using critical point theory. Furthermore, based on the strong maximum principle, we prove that the three solutions are positive under appropriate nonlinear...
| Published in: | Boundary Value Problems |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-02-01
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| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01588-z |
| _version_ | 1857057171964952576 |
|---|---|
| author | Feng Xiong Zhan Zhou |
| author_facet | Feng Xiong Zhan Zhou |
| author_sort | Feng Xiong |
| collection | DOAJ |
| container_title | Boundary Value Problems |
| description | Abstract In this paper, we prove the existence of three solutions to a partial difference equation with ( p , q ) $(p,q)$ -Laplacian operator by using critical point theory. Furthermore, based on the strong maximum principle, we prove that the three solutions are positive under appropriate nonlinearity assumptions. Finally, we also give an example to illustrate our main results. |
| format | Article |
| id | doaj-art-8b94de8a43184bce92e555c9a22ffb18 |
| institution | Directory of Open Access Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2022-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| spelling | doaj-art-8b94de8a43184bce92e555c9a22ffb182025-08-19T19:30:44ZengSpringerOpenBoundary Value Problems1687-27702022-02-012022111310.1186/s13661-022-01588-zThree positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operatorFeng Xiong0Zhan Zhou1School of Mathematics and Information Science, Guangzhou UniversitySchool of Mathematics and Information Science, Guangzhou UniversityAbstract In this paper, we prove the existence of three solutions to a partial difference equation with ( p , q ) $(p,q)$ -Laplacian operator by using critical point theory. Furthermore, based on the strong maximum principle, we prove that the three solutions are positive under appropriate nonlinearity assumptions. Finally, we also give an example to illustrate our main results.https://doi.org/10.1186/s13661-022-01588-zBoundary value problemThree positive solutionsPartial difference equation( p , q ) $(p,q)$ -LaplacianCritical point theory |
| spellingShingle | Feng Xiong Zhan Zhou Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator Boundary value problem Three positive solutions Partial difference equation ( p , q ) $(p,q)$ -Laplacian Critical point theory |
| title | Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator |
| title_full | Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator |
| title_fullStr | Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator |
| title_full_unstemmed | Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator |
| title_short | Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator |
| title_sort | three positive solutions for a nonlinear partial discrete dirichlet problem with p q p q laplacian operator |
| topic | Boundary value problem Three positive solutions Partial difference equation ( p , q ) $(p,q)$ -Laplacian Critical point theory |
| url | https://doi.org/10.1186/s13661-022-01588-z |
| work_keys_str_mv | AT fengxiong threepositivesolutionsforanonlinearpartialdiscretedirichletproblemwithpqpqlaplacianoperator AT zhanzhou threepositivesolutionsforanonlinearpartialdiscretedirichletproblemwithpqpqlaplacianoperator |