Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator
Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/14/1691 |
| _version_ | 1797526693864275968 |
|---|---|
| author | Shaohong Wang Zhan Zhou |
| author_facet | Shaohong Wang Zhan Zhou |
| author_sort | Shaohong Wang |
| collection | DOAJ |
| description | Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results. |
| first_indexed | 2024-03-10T09:32:59Z |
| format | Article |
| id | doaj.art-fd0d8b9e3b2e4351bf3eeaae8e296c1f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:32:59Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fd0d8b9e3b2e4351bf3eeaae8e296c1f2023-11-22T04:20:43ZengMDPI AGMathematics2227-73902021-07-01914169110.3390/math9141691Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature OperatorShaohong Wang0Zhan Zhou1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaPartial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results.https://www.mdpi.com/2227-7390/9/14/1691Dirichlet boundary value problempartial difference equationthe mean curvature operatorcritical point theory |
| spellingShingle | Shaohong Wang Zhan Zhou Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator Mathematics Dirichlet boundary value problem partial difference equation the mean curvature operator critical point theory |
| title | Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator |
| title_full | Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator |
| title_fullStr | Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator |
| title_full_unstemmed | Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator |
| title_short | Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator |
| title_sort | three solutions for a partial discrete dirichlet problem involving the mean curvature operator |
| topic | Dirichlet boundary value problem partial difference equation the mean curvature operator critical point theory |
| url | https://www.mdpi.com/2227-7390/9/14/1691 |
| work_keys_str_mv | AT shaohongwang threesolutionsforapartialdiscretedirichletprobleminvolvingthemeancurvatureoperator AT zhanzhou threesolutionsforapartialdiscretedirichletprobleminvolvingthemeancurvatureoperator |