A Singular Semilinear Elliptic Equation with a Variable Exponent

In this paper we consider singular semilinear elliptic equations with a variable exponent whose model problem is Here Ω is an open bounded set of , is a positive continuous function and is a positive function that belongs to a certain Lebesgue space. We prove that there exists a solution to this pro...

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Bibliographic Details
Published in:Advanced nonlinear studies 2016-08, Vol.16 (3), p.491-498
Main Authors: Carmona, José, Martínez-Aparicio, Pedro J.
Format: Article
Language:English
Subjects:
35A01
35B09
35B45
35D30
35J25
35J61
35J75
Existence
Positive Solutions
Semilinear Equations
Singularity
Variable Exponent
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Summary:In this paper we consider singular semilinear elliptic equations with a variable exponent whose model problem is Here Ω is an open bounded set of , is a positive continuous function and is a positive function that belongs to a certain Lebesgue space. We prove that there exists a solution to this problem in the natural energy space when in a strip around the boundary. For another case, we prove that the solution belongs to and that it is zero on the boundary in a suitable sense.
ISSN:1536-1365
2169-0375
DOI:10.1515/ans-2015-5039