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1.
Let Ω RN be a ball centered at the origin with radius R > 0 and N 7, 2* = 2N/N-2. We obtain the existence of infinitely many radial solutions for the Dirichlet problem -△u = μ |x|2 u |u|2*-2u λu in Ω, u = 0 on аΩ for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.  相似文献   

2.
Let be a ball centered at the origin with radius R. We investigate the asymptotic behavior of positive solutions for the Dirichlet problem in on ∂BR when ɛ→+ for suitable positive numbers μ Mathematics Subject Classification (2000) 35J60, 35B33  相似文献   

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In this paper, we establish a global compactness result for (P.S.) sequences of the variational functional of the elliptic problem Δuμ|x|2u=1|x|s|u|2s12u+λu,xΩ,u=0onΩ,where ΩRn, n3, is a bounded smooth domain with 0Ω, μ[0,(n2)24), s[0,2) and λR are constants. This extends the global compactness result of Cao and Peng (2003) to the case of elliptic problems with double singular critical terms. Our arguments adapt some refined Sobolev inequalities systematically developed quite recently by Palatucci and Pisante (2014) and blow-up analysis. In this way, our arguments turn out to be quite transparent and easy to be applied to many other problems.  相似文献   

5.
Let be a bounded domain such that . We obtain existence of sign-changing solutions for the Dirichlet problem on Ω,u=0 on ∂Ω for suitable positive numbers μ and λ.  相似文献   

6.
This paper is devoted to the existence of solutions for a singular critical semilinear elliptic equation. Some existence and multiplicity results are obtained by using mountain pass arguments and analysis techniques. The results of Ding and Tang (2007) and Kang (2007) and related are improved.  相似文献   

7.
This paper deals with the following class of singular biharmonic problems
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8.
In this paper we consider the existence and multiplicity of positive weak solutions for a class of elliptic problems with the nonlinearity containing both singular and critical terms. By means of the concentration compactness principle due to Lions and Ekeland’s variational principle, two positive weak solutions are obtained.  相似文献   

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In this paper, we study a class of semilinear elliptic equations with Hardy potential and critical Sobolev exponent. By means of the Ekeland variational principle and Mountain Pass theorem, multiple positive solutions are obtained.  相似文献   

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