Boundary value problems for a second-order difference equation involving the mean curvature operator
Abstract In this paper, we consider the existence of multiple solutions for discrete boundary value problems involving the mean curvature operator by means of Clark’s Theorem, where the nonlinear terms do not need any asymptotic and superlinear conditions at 0 or at infinity. Further, the existence...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01637-7 |
| _version_ | 1811315268695097344 |
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| author | Zhenguo Wang Qilin Xie |
| author_facet | Zhenguo Wang Qilin Xie |
| author_sort | Zhenguo Wang |
| collection | DOAJ |
| description | Abstract In this paper, we consider the existence of multiple solutions for discrete boundary value problems involving the mean curvature operator by means of Clark’s Theorem, where the nonlinear terms do not need any asymptotic and superlinear conditions at 0 or at infinity. Further, the existence of a positive solution has been considered by the strong comparison principle. As an application, some examples are given to illustrate the obtained results. |
| first_indexed | 2024-04-13T11:27:15Z |
| format | Article |
| id | doaj.art-35429738c99349d1a1e71f2c30b090a0 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-13T11:27:15Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-35429738c99349d1a1e71f2c30b090a02022-12-22T02:48:39ZengSpringerOpenBoundary Value Problems1687-27702022-08-012022111310.1186/s13661-022-01637-7Boundary value problems for a second-order difference equation involving the mean curvature operatorZhenguo Wang0Qilin Xie1School of Mathematics and Statistics, Huanghuai UniversitySchool of Mathematics and Statistics, Guangdong University of TechnologyAbstract In this paper, we consider the existence of multiple solutions for discrete boundary value problems involving the mean curvature operator by means of Clark’s Theorem, where the nonlinear terms do not need any asymptotic and superlinear conditions at 0 or at infinity. Further, the existence of a positive solution has been considered by the strong comparison principle. As an application, some examples are given to illustrate the obtained results.https://doi.org/10.1186/s13661-022-01637-7Discrete boundary value problemsMean curvature operatorPalais–Smale conditionCritical-point theory |
| spellingShingle | Zhenguo Wang Qilin Xie Boundary value problems for a second-order difference equation involving the mean curvature operator Boundary Value Problems Discrete boundary value problems Mean curvature operator Palais–Smale condition Critical-point theory |
| title | Boundary value problems for a second-order difference equation involving the mean curvature operator |
| title_full | Boundary value problems for a second-order difference equation involving the mean curvature operator |
| title_fullStr | Boundary value problems for a second-order difference equation involving the mean curvature operator |
| title_full_unstemmed | Boundary value problems for a second-order difference equation involving the mean curvature operator |
| title_short | Boundary value problems for a second-order difference equation involving the mean curvature operator |
| title_sort | boundary value problems for a second order difference equation involving the mean curvature operator |
| topic | Discrete boundary value problems Mean curvature operator Palais–Smale condition Critical-point theory |
| url | https://doi.org/10.1186/s13661-022-01637-7 |
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