Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions

In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ = λ ) ± ) under Robin boundary condition in a regular open bounded domain Ω of ℝ , ≥ 2. Δ is the )-Laplacian operator where ∈ ) and > 1. Our proofs are based on the sub solutio...

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Bibliographic Details
Published inMathematica Slovaca Vol. 72; no. 6; pp. 1541 - 1550
Main Authors Dammak, Makkia, Ali, Abir Amor Ben
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 16.12.2022
Walter de Gruyter GmbH
Subjects
35J60
35J70
35K57
Boundary conditions
Coercivity
generalised Sobolev spaces
Laplace operator
Primary 35J20
quasilinear equation
sub solution-super solution method
variational methods
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Summary:In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ = λ ) ± ) under Robin boundary condition in a regular open bounded domain Ω of ℝ , ≥ 2. Δ is the )-Laplacian operator where ∈ ) and > 1. Our proofs are based on the sub solution-super solution method and also on variational arguments.
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2022-0105