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1.
This paper concerns the following nonlinear elliptic equation:{?u + K(y)u~((N+2)/(N-2)±ε)= 0, u 0, y ∈ R~N,u ∈ D~(1,2)(R~N),where ε 0, N≥5, K(y) is positive and radially symmetric. We show that, under some local conditions on K(y), this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2),there exists solutions whose functional energy is in the order of ε~(-(N-2-m)/((N-2)~2)).  相似文献   

2.
In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/(N-2) is the critical Sobolev exponent, 2 q 2 , 0≤μ μˉ=(N-2)2_4 , a(x), k(x) ∈ C(RN ). Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a(x) and k(x).  相似文献   

3.
Let f: S~1→M~2 or M~2→N~3 be a map, we classify the immersions homotopic to f, where M~2 and N~3 are arbitrary surface and 3-manifolds respectively.  相似文献   

4.
Let Ω be a bounded smooth domain in RN(N≥3).Assuming that 0 0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,■Under some assumptions of hi(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1) by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establis...  相似文献   

5.
设(M~(4n k 2),T)是一个带有光滑对合T的光滑闭流形,T的不动点集为RP(4)■ P(4,2n-1).本文决定了(M~(4n k 2),T)的所有协边类.  相似文献   

6.
In this article, we study the nonexistence of solution with finite Morse index for the following Choquard type equation-△u=∫RN|u(y)|p|x-y|αdy|u(x)|p-2u(x) in RN where N ≥ 3, 0 α min{4, N}. Suppose that 2 p (2 N-α)/(N-2),we will show that this problem does not possess nontrivial solution with finite Morse index. While for p=(2 N-α)/(N-2),if i(u) ∞, then we have ∫_RN∫_RN|u(x)p(u)(y)~p/|x-y|~α dxdy ∞ and ∫_RN|▽u|~2 dx=∫_RN∫_RN|u(x)p(u)(y)~p/|x-y|~αdxdy.  相似文献   

7.
关于n维微分流形M~n(n≥2)上的系统的结构稳定性问题已在[1]中作了精辟的论述。我们这里只介绍n=2时的一部分情况。 1.1结构稳定性 命M~2为一个列紧(无边界的)连通的C~∞型二维流形。(?)~r(M~2)(r=1,2,3,…)为定义在M~2上所有至少是C~r类的常微系统(即C~r切向量场)作成的集合。为讨论(?)~r(M~2)中的系统的扰动问题,我们必须在其中引进度量。为此,我们简单地取定M~2上的一组局部坐标系。在M~2上给出有限的开复盖U_(aj)(j=1,2,…,s)之后,对于X∈(?)~r(M~2),我们  相似文献   

8.
In this paper, we prove that for-1/2 ≤β≤0.suppose M is an invariant subspaces of the Hardy Sobolev spaces H_β~2(D) for T_z~β, then M() zM is a generating wandering subspace of M, that is,M=[MzM]_T_z~β Moreover, any non-trivial invariant subspace M of H_β~2(D) is also generated by the quasi-wandering subspace P_MT_z~βM~⊥ that is,M=[P_MT_z~βM~⊥]_(T_z~β).  相似文献   

9.
§ 1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space W_t~2~(1,2)(O, +∞) into L_t~2~q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2~*=2N/N-2 is the critical exponent of the Sobolev embedding H~1(R~n)→L~Q(R~N). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|~(l-1)u+f(u) is lower then |u|~(v+3/v-1) i.e.  相似文献   

10.
Let M and M~* be hypersurfaces in an affine space A~(n+1) of dimension n+1. The main results of this paper are the following:(1) Two types of integral formulas for M and M~*.(2) Some conditions for an affine convex hypersurface to be an affine sphere.(3) Some conditions for M and M~* to be different only by an affine transformation or a translation.  相似文献   

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