Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 66, Issue 7, Pages 1485-1497Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2006.02.005
Keywords
p-Laplacian operator; critical Sobolev exponent; Palais-Smale condition; Mountain Pass Theorem; concentration-compactness principle
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We study here a class of quasilinear elliptic systems involving the p-Laplacian operator; the right hand sides of systems are closely related to the critical Sobolev exponents. Under some additional assumptions on the nonlinearities, the corresponding functional verifies the Palais-Smale condition (PS)(c) for c belonging to a specified range. So, we can use the Mountain Pass Theorem to prove the existence of at least one nontrivial solution. (c) 2006 Elsevier Ltd. All rights reserved.
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