This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corr...This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.展开更多
The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation ?Δu = |x| α u p?1, u > 0, x ∈ B R (0) ? ? n (n ? 3), u = 0, x ∈ ?B R (0), where $ p \to p(\alph...The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation ?Δu = |x| α u p?1, u > 0, x ∈ B R (0) ? ? n (n ? 3), u = 0, x ∈ ?B R (0), where $ p \to p(\alpha ) = \frac{{2(n + \alpha )}} {{n - 2}} $ from left side, α > 0.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10771219, 11071092)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20100144110001)
文摘This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.
基金supported by National Natural Science Foundation of China (Grant No. 10631030)the Program for New Century Excellent Talents in University (Grant No. 07-0350)+1 种基金the Key Project of ChineseMinistry of Education (Grant No. 107081)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Chinese Ministry of Education
文摘The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation ?Δu = |x| α u p?1, u > 0, x ∈ B R (0) ? ? n (n ? 3), u = 0, x ∈ ?B R (0), where $ p \to p(\alpha ) = \frac{{2(n + \alpha )}} {{n - 2}} $ from left side, α > 0.
