Results on multiple nontrivial solutions to partial difference equations
In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreov...
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| Formaat: | Artikel |
| Taal: | English |
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AIMS Press
2023-01-01
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| Reeks: | AIMS Mathematics |
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| Online toegang: | https://www.aimspress.com/article/doi/10.3934/math.2023272?viewType=HTML |
| _version_ | 1828052477572808704 |
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| author | Huan Zhang Yin Zhou Yuhua Long |
| author_facet | Huan Zhang Yin Zhou Yuhua Long |
| author_sort | Huan Zhang |
| collection | DOAJ |
| description | In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreover, we provide five examples to illustrate applications of our theorems. |
| first_indexed | 2024-04-10T19:53:11Z |
| format | Article |
| id | doaj.art-be9e16b87c6a41f8b51bf82eef312cad |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T19:53:11Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-be9e16b87c6a41f8b51bf82eef312cad2023-01-28T01:29:19ZengAIMS PressAIMS Mathematics2473-69882023-01-01835413543110.3934/math.2023272Results on multiple nontrivial solutions to partial difference equationsHuan Zhang 0Yin Zhou1Yuhua Long21. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China 2. Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou, 510006, China3. Transportation and Economics Research Institute of China Academy of Railway Sciences Corporation Limited, Beijing, 100081, China1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China 2. Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou, 510006, ChinaIn this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreover, we provide five examples to illustrate applications of our theorems.https://www.aimspress.com/article/doi/10.3934/math.2023272?viewType=HTMLpartial difference equationlocal linkingmorse theorynontrivial solution |
| spellingShingle | Huan Zhang Yin Zhou Yuhua Long Results on multiple nontrivial solutions to partial difference equations AIMS Mathematics partial difference equation local linking morse theory nontrivial solution |
| title | Results on multiple nontrivial solutions to partial difference equations |
| title_full | Results on multiple nontrivial solutions to partial difference equations |
| title_fullStr | Results on multiple nontrivial solutions to partial difference equations |
| title_full_unstemmed | Results on multiple nontrivial solutions to partial difference equations |
| title_short | Results on multiple nontrivial solutions to partial difference equations |
| title_sort | results on multiple nontrivial solutions to partial difference equations |
| topic | partial difference equation local linking morse theory nontrivial solution |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023272?viewType=HTML |
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