Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for all small values of the parameter {\lambda} > 0, there exis...

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Bibliographic Details
Published inarXiv.org
Main Authors Aberqi, Ahmed, Bennouna, Jaouad, Benslimane, Omar, Ragusa, Maria Alessandra
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.01.2022
Subjects
Exponents
Manifolds
Sobolev space
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Summary:The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for all small values of the parameter {\lambda} > 0, there exist at least two non-trivial positive solutions. Our results extend the previous works Papageorgiou, Repov\u{s}, and Vetro [24] and Liu, Dai, Papageorgiou, and Winkert [21], from the case of Musielak-Orlicz Sobolev space, when exponents p and q are constant, to the case of Sobolev-Orlicz spaces with variable exponents in a complete manifold.
ISSN:2331-8422