POSITIVELY CURVED COMPLETE NONCOMPACT KAHLER MANIFOLDS

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. Among other things, we prove that a complete noncompact Kahler surface with positive and bounded sectional curvature and with finite analytic Chern number c1（M）^2 is biholomorphic to C2.     

ON THE EXISTENCE OF NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM FOR UNBOUNDED DOMAINS (2) Zero Mass Case

§0. Introduction In this paper, we continue studying the existence problem: The main difficulty we meet is generally lack of compact Sobolev embedding on unbounded domains. For the case of positive mass, we have proved in [1] the functional corresponding to (0.1) partially satisfies (P. S)_0 condition, then we may get nontrivial selution by Mountain Pass lemma. Here we shall give similar results for the case of zero mass.     

NONTRIVIAL SOLUTION OF NONLINEAR SCALAR FIELD EQUATIONS WITH STRONG NONLINEARITY

In this paper, we use the concentration-compactness prieciple togther with the Mountain Pass Lemma to get the existence of nontrivial solutions of the following scalar field equations with strong nonlinearity     

临界增长拟线性椭圆型方程的非平凡解

本文给出R^N中有界域Ω上拟线性临界增长椭圆型方程的Dirichlet问题的非平凡W^1,p(Ω)广义解的存在性结果。     

临界增长半线性椭圆型方程的多解性

注1 λ_1是算子L关于Dirichlet条件的第一个特征值,我们粗略地称f(x,u)为λ|u|~(p-1)u的超线性低阶微扰。 我们注意到p+1=(2n)/(n-2)是Sobolev嵌入H'_0→L~(p+1)的临界指数,此时嵌入不是紧致的,对应的变分泛函不满足(ps)条件,这将给用通常的对偶变分理论来处理(1)的多解性造成了很大困难。当p<(n+2)/(n-2)时,Ambrosetti-Rabinowitz的著名结果已经给出了     

ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS

§1. Introduction In this paper, we consider the problem     

BIFURCATION FOR ELLIPTIC EQUATIONS ON UNBOUNDED DOMAINS

In this paper we study the bifurcation problem for the following elliptic equalion (0.1) Here Lu= -△u has no eigenvalues and has only essential spectrum in R~N, the usual Lyapunov-Schmidt reduction cannot be used in problem (0.1). Meanwhile, L is not compact in H~1(R~N), of course, the method of topological degree is also     

Positive Solution of Nonlinear Elliptic Equation (Critical Exponent Case)

In this paper we study Dirichlet problem: u>0 x∈Ω, u=0 x∈ Ω,Where 1)Ω is a bounded domain in R~n(n≥3),(a_(ij)(x))is positive definite onΩ,a_(ij)(x)∈c~∞(Ω). 2)h(x,u):Ω×(Q,∞)→R is smooth in x,continuous in u,h(x,0)=0 andassume uniformly in x, uniformly in x, and b(x)>0 on Ω.tain the following results.     

R~N 上半线性椭圆型方程的多解性

本文给出了 R~n 上半线性椭圆型方程的两对非平凡解存在结果.     

ON THE EXISTENCE OF NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM FOR UNBOUNDED DOMAINS (Ⅰ) Positive Mass Case

§0. Introduction This paper as well as the subsequent one is concerned with the existence of nontrivial solution on unbounded domains for quasilinear elliptic equation: with zero-Dirichlet condition. Its energy functional is