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Zbl 1192.35080
Da Silva Rodrigues, Rodrigo
On elliptic problems involving critical Hardy-Sobolev exponents and sign-changing function. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 4, 857-880 (2010). ISSN 0362-546X

Summary: We deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nehari manifold and by exploring some properties of the best Hardy-Sobolev constant together with an approach developed by Brezis and Nirenberg.

MSC 2000:: *35J70 Elliptic equations of degenerate type
35A15 Variational methods (PDE)
35B33 Critical exponents
35J62
35D30
35J20 Second order elliptic equations, variational methods

Keywords: quasilinear elliptic equations; Nehari manifolds; critical Hardy-Sobolev exponent

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Zentralblatt MATH Berlin [Germany]