We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution fo...We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.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
In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic...In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.展开更多
Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu }...Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u $ in Ω, u = 0 on ?Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.展开更多
We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
基金supported by Postdoctoral Science Foundation of China, National Natural Science Foundationof China (No. 10631020, 10871061)the Grant for PhD Program of Ministry of Education of China
文摘We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ?2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.
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.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10531020)the Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007).
文摘In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.
基金supported by the National Natural Science Foundation of China (Grant No. 10526008)
文摘Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u $ in Ω, u = 0 on ?Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.
基金the National Natural Science Foundation of China (Grant No. 10671049), Longjiang Scholar GrantScience Research Fund of the Education Department of Heilongjiang Province (Grant No.11531246)Harbin Normal University Academic Backbone of Youth Project
文摘We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
