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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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Bibliographic Details
Published in:Applied mathematics & optimization 2024-08, Vol.90 (1), p.13, Article 13
Main Authors: Liu, Wulong, Dai, Guowei, Winkert, Patrick, Zeng, Shengda
Format: Article
Language:English
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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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10155-0