Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian
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 &l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2030 |
| _version_ | 1797547932460777472 |
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| author | Sijia Du Zhan Zhou |
| author_facet | Sijia Du Zhan Zhou |
| author_sort | Sijia Du |
| collection | DOAJ |
| description | 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 <i>p</i>-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. |
| first_indexed | 2024-03-10T14:51:11Z |
| format | Article |
| id | doaj.art-c885f56ff313434e97899dfbbd3fba43 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:51:11Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c885f56ff313434e97899dfbbd3fba432023-11-20T20:58:14ZengMDPI AGMathematics2227-73902020-11-01811203010.3390/math8112030Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-LaplacianSijia Du0Zhan Zhou1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaDue 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 <i>p</i>-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.https://www.mdpi.com/2227-7390/8/11/2030partial difference equationsboundary value problemp-laplacianmultiple solutionscritical point theory |
| spellingShingle | Sijia Du Zhan Zhou Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian Mathematics partial difference equations boundary value problem p-laplacian multiple solutions critical point theory |
| title | Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian |
| title_full | Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian |
| title_fullStr | Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian |
| title_full_unstemmed | Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian |
| title_short | Multiple Solutions for Partial Discrete Dirichlet Problems Involving the <i>p</i>-Laplacian |
| title_sort | multiple solutions for partial discrete dirichlet problems involving the i p i laplacian |
| topic | partial difference equations boundary value problem p-laplacian multiple solutions critical point theory |
| url | https://www.mdpi.com/2227-7390/8/11/2030 |
| work_keys_str_mv | AT sijiadu multiplesolutionsforpartialdiscretedirichletproblemsinvolvingtheipilaplacian AT zhanzhou multiplesolutionsforpartialdiscretedirichletproblemsinvolvingtheipilaplacian |