Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
نویسندگان
چکیده
منابع مشابه
Multiple Solutions for Quasi-linear Pdes Involving the Critical Sobolev and Hardy Exponents
We use variational methods to study the existence and multiplicity of solutions for the following quasi-linear partial differential equation: ( −4pu = λ|u|r−2u+ μ |u| q−2 |x|s u in Ω, u|∂Ω = 0, where λ and μ are two positive parameters and Ω is a smooth bounded domain in Rn containing 0 in its interior. The variational approach requires that 1 < p < n, p ≤ q ≤ p∗(s) ≡ n−s n−pp and p ≤ r ≤ p ∗ ≡...
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In this paper, by using concentration-compactness principle and a new version of the symmetric mountain-pass lemma due to Kajikiya (J Funct Anal 225:352–370, 2005), infinitely many small solutions are obtained for a class of quasilinear elliptic equation with singular potential −∆pu− μ |u| p−2u |x|p = |u|p(s)−2u |x|s + λf(x, u), u ∈ H 1,p 0 (Ω). Mathematics Subject Classification (2000). 35J60,...
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متن کاملSolutions 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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2000
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-00-02560-5