Existence Results for Double Phase Problem in Sobolev–Orlicz Spaces with Variable Exponents in Complete Manifold

In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti–Rabinowitz type condition in the framework of Sobolev–Orlicz spaces with variable exponents in complete mani...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 19; no. 4
Main Authors Aberqi, Ahmed, Bennouna, Jaouad, Benslimane, Omar, Ragusa, Maria Alessandra
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2022
Springer Nature B.V
Subjects
Exponents
Manifolds
Mathematics
Mathematics and Statistics
Primary 35J20
35J60
Sobolev–Orlicz Riemannian manifold
Nehari manifold
Secondary 35J47
Existence solutions
double phase problem
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Summary:In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti–Rabinowitz type condition in the framework of Sobolev–Orlicz spaces with variable exponents in complete manifold. Our approach is based on the Nehari manifold and some variational techniques. Furthermore, the Hölder ine-quality, continuous and compact embedding results are proved.
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ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-022-02097-0