Multiplicity of solutions for singular semilinear elliptic equations with critical Hardy-Sobolev exponents

Multiplicity of Solutions for Singular Semilinear Elliptic Equations with Critical Hardy-sobolev Exponents

where Ω ⊂ R(N ≥ 4) is an open bounded domain with smooth boundary, β > 0, 0 ∈ Ω, 0 ≤ s < 2, 2∗(s) := 2(N − s) N − 2 is the critical Hardy-Sobolev exponent and, when s = 0, 2∗(0) = 2N N − 2 is the critical Sobolev exponent, 0 ≤ μ < μ := (N − 2) 4 . In [1] A. Ferrero and F. Gazzola investigated the existence of nontrivial solutions for problem (1.1) with β = 1, s = 0. In [2] D. S. Kang and S. J. ...

Solutions for semilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy potential

Let Ω ⊂ RN be a smooth bounded domain such that 0 ∈ Ω , N ≥ 5, 0 ≤ s < 2, 2∗(s) = 2(N−s) N−2 . We prove the existence of nontrivial solutions for the singular critical problem − u − μ u |x |2 = |u| 2∗(s)−2 |x |s u + λu with Dirichlet boundary condition on Ω for all λ > 0 and 0 ≤ μ < ( N−2 2 )2 − ( N+2 N )2. © 2005 Elsevier Ltd. All rights reserved. MSC: 35J60; 35B33

On Multiple Solutions for a Singular Quasilinear Elliptic System Involving Critical Hardy-sobolev Exponents

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

Multiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities

and Applied Analysis 3 When a 0, we set s dp∗ 0, d and t bp∗ 0, b , then 1.1 is equivalent to the following quasilinear elliptic equations: −div ( |∇u|p−2∇u ) − μ |u| p−2u |x| |u|p t −2u |x| λ |u|q−2u |x| in Ω, u 0 on ∂Ω, 1.7 where λ > 0, 1 < p < N, 0 ≤ μ < μ N − p /p , 0 ≤ s, t < p, 1 ≤ q < p and p∗ t p N − t / N − p . Such kind of problem relative with 1.7 has been extensively studied by many...

Nodal Solutions of Elliptic Equations with Critical Sobolev Exponents