Multiple solutions with sign information for Robin equations with indefinite potential
In this paper, we study a Robin boundary value problem driven by the Laplace operator plus an indefinite potential term. The reaction is of the logistic type. Using variational methods together with truncations, comparisons and critical groups, we prove two multiplicity theorems producing smooth sol...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2025-04-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360724500139 |
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| author | Nikolaos S. Papageorgiou Jian Zhang Wen Zhang |
| author_facet | Nikolaos S. Papageorgiou Jian Zhang Wen Zhang |
| author_sort | Nikolaos S. Papageorgiou |
| collection | DOAJ |
| description | In this paper, we study a Robin boundary value problem driven by the Laplace operator plus an indefinite potential term. The reaction is of the logistic type. Using variational methods together with truncations, comparisons and critical groups, we prove two multiplicity theorems producing smooth solutions with sign information. A special case, which we encounter in the literature, is also considered. |
| format | Article |
| id | doaj-art-8fa436ffbaaf4091908964118929a12e |
| institution | OA Journals |
| issn | 1664-3607 1664-3615 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj-art-8fa436ffbaaf4091908964118929a12e2025-08-20T02:26:28ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152025-04-01150110.1142/S1664360724500139Multiple solutions with sign information for Robin equations with indefinite potentialNikolaos S. Papageorgiou0Jian Zhang1Wen Zhang2Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, GreeceSchool of Mathematics and Statistics, Hunan University of Technology and Business, 410205 Changsha, Hunan, P. R. ChinaSchool of Mathematics and Statistics, Hunan University of Technology and Business, 410205 Changsha, Hunan, P. R. ChinaIn this paper, we study a Robin boundary value problem driven by the Laplace operator plus an indefinite potential term. The reaction is of the logistic type. Using variational methods together with truncations, comparisons and critical groups, we prove two multiplicity theorems producing smooth solutions with sign information. A special case, which we encounter in the literature, is also considered.https://www.worldscientific.com/doi/10.1142/S1664360724500139Indefinite potentialRobin boundary conditiontruncationsHopf maximum principleconstant sign and nodal solutionscritical groups |
| spellingShingle | Nikolaos S. Papageorgiou Jian Zhang Wen Zhang Multiple solutions with sign information for Robin equations with indefinite potential Bulletin of Mathematical Sciences Indefinite potential Robin boundary condition truncations Hopf maximum principle constant sign and nodal solutions critical groups |
| title | Multiple solutions with sign information for Robin equations with indefinite potential |
| title_full | Multiple solutions with sign information for Robin equations with indefinite potential |
| title_fullStr | Multiple solutions with sign information for Robin equations with indefinite potential |
| title_full_unstemmed | Multiple solutions with sign information for Robin equations with indefinite potential |
| title_short | Multiple solutions with sign information for Robin equations with indefinite potential |
| title_sort | multiple solutions with sign information for robin equations with indefinite potential |
| topic | Indefinite potential Robin boundary condition truncations Hopf maximum principle constant sign and nodal solutions critical groups |
| url | https://www.worldscientific.com/doi/10.1142/S1664360724500139 |
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