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Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains
In this paper we prove the existence of multiple positive solutions for a quasilinear elliptic problem with unbalanced growth in expanding domains by using variational methods and the Lusternik–Schnirelmann category theory. Based on the properties of the category, we introduce suitable maps between...
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Published in: | Applied mathematics & optimization 2024-08, Vol.90 (1), p.13, Article 13 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | In this paper we prove the existence of multiple positive solutions for a quasilinear elliptic problem with unbalanced growth in expanding domains by using variational methods and the Lusternik–Schnirelmann category theory. Based on the properties of the category, we introduce suitable maps between the expanding domains and the critical levels of the energy functional related to the problem, which allow us to estimate the number of positive solutions by the shape of the domain. |
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ISSN: | 0095-4616 1432-0606 |
DOI: | 10.1007/s00245-024-10155-0 |