Solutions to critical elliptic equations with multi-singular inverse square potentials
By Daomin Cao, Pigong Han. 2006
105 citations recorded by the source corpus.
Abstract Let Ω be an open-bounded domain in R N ( N ⩾ 3 ) with smooth boundary ∂ Ω . We are concerned with the multi-singular critical elliptic problem - Δ u - ∑ i = 1 k μ i u | x - a i | 2 = Q ( x ) | u | 2 * - 2 u , u ∈ H 0 1 ( Ω ) , ( * ) where μ i ∈ R , 2 * = 2 N N - 2 , a i ∈ Ω ( 1 ⩽ i ⩽ k ) and Q ( x ) is a positive bounded function on Ω ¯ . Using Moser iteration, we prove the asymptotic behavior of solutions for ( * ) at points a i ( 1 ⩽ i ⩽ k ) . By exploiting the effect of the coefficient of the critical nonlinearity, we, by means of a variational method, establish the existence of positive and sign-changing solutions for problem ( * ) .
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/701bcd17b46da126d9983ba522b48789ce170bf1
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In Applied Mathematics
- Chang-Lin Xiang
- Shusen Yan
- Daomin Cao
- Dongsheng Kang
- Y. Huang
- Shuangjie Peng
- Jun-cheng Wei
- Xiaohui Yu
In Computational Theory and Mathematics
In Mathematical Physics
- Chang-Lin Xiang
- Shusen Yan
- Dongsheng Kang
- Daomin Cao
- Y. Huang
- Shuangjie Peng
- Jun-cheng Wei
- Changshou Lin
Citations in the corpus
- Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential (2010, background): “Similar to the proof of Theorem 1.1 in [ 9 ], we can deduce”
- Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential (2015, background): “s both a weak subsolution and a weak supersolution. Equation (1.1) and its variants have been extensively studied in the literature. For the existence of solutions to equation (1.1), we refer to e.g. [3, 4, 7, 8, 9, 10, 11, 16, 17, 19, 20, 26]. For the uniqueness of solutions to equation (1.1), we r”
- On the singular elliptic systems involving multiple critical Sobolev exponents (2011, background): “See for example [6–8,4,9–15,3] and the references therein.”