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On elliptic problems involving critical Hardy-Sobolev exponents and sign-changing function. (English) Zbl 1192.35080
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:
35J70Degenerate elliptic equations
35A15Variational methods (PDE)
35B33Critical exponents (PDE)
35J62Quasilinear elliptic equations
35D30Weak solutions of PDE
35J20Second order elliptic equations, variational methods
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Full Text: DOI
References:
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