Moderate solutions of semilinear elliptic equations with Hardy potential
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Solutions to Semilinear Elliptic Equations with Hardy Potential
Let Ω be an open bounded domain in RN (N ≥ 3) with smooth boundary ∂Ω, 0 ∈ Ω. We are concerned with the asymptotic behavior of solutions for the elliptic problem: (∗) −∆u− μu |x|2 = f(x, u), u ∈ H 0 (Ω), where 0 ≤ μ < ( N−2 2 )2 and f(x, u) satisfies suitable growth conditions. By Moser iteration, we characterize the asymptotic behavior of nontrivial solutions for problem (∗). In particular, we...
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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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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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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2017
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2015.10.001