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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.

35J70Degenerate elliptic equations
35A15Variational methods (PDE)
35B33Critical exponents (PDE)
35J62Quasilinear elliptic equations
35D30Weak solutions of PDE
35J20Second order elliptic equations, variational methods
Full Text: DOI
[1] Brezis, H.; Nirenberg, L.: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. pure appl. Math. 36, 437-477 (1983) · Zbl 0541.35029 · doi:10.1002/cpa.3160360405
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