Journal
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Volume 37, Issue 2, Pages 579-594Publisher
SUOMALAINEN TIEDEAKATEMIA
DOI: 10.5186/aasfm.2012.3743
Keywords
Sobolev embedding; variable exponents; critical exponents; concentration compactness
Categories
Funding
- Universidad de Buenos Aires [X078]
- CONICET (Argentina) [PIP 5478/1438]
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In this paper we study the existence problem for the p(x)-Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration-Compactness Principle for variable exponents and the Mountain Pass Theorem.
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