Positive Radial Solutions for a Class of Semilinear Elliptic Problems Involving Critical Hardy-Sobolev Exponent and Hardy Terms
نویسندگان
چکیده
منابع مشابه
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
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In the present paper, a quasilinear elliptic problem with a critical Sobolev exponent and a Hardy-type term is considered. By means of a variational method, the existence of nontrivial solutions for the problem is obtained. The result depends crucially on the parameters p, t, s, λ and μ. c © 2007 Elsevier Ltd. All rights reserved. MSC: 35J60; 35B33
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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. ...
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where B1 = {x ∈ RN | |x| < 1} is the unit ball in RN (N ≥ 3), λ, μ > 0, 2∗ := 2N/(N − 2). When μ < 0, this problem has been considered by many authors recently (cf. [5, 6, 7, 8]). But when μ > 0, this problem has not been considered as far as we know. In fact, the existence of nontrivial solution for (1.1) when μ > 0 is an open problem which was imposed in [7]. In this paper, we get the followi...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Physics
سال: 2017
ISSN: 2327-4352,2327-4379
DOI: 10.4236/jamp.2017.511180