YAMABE PROBLEM IN R~n AND RELATED PROBLEMS

This paper is concerned with the existence of positive solution of the Yamabe problem in R~n.     

ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we prove the existence of k-node solution of singular nonlinear boundary value problems for each k∈N ∪ {0}.     

EIGENFUNCTIONS OF THE NONLINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT IN R~2

We consider the following eigenvalue problem: Where f(x, t) is a continuous function with critical growth. We prove the existence of nontrivial solutions.     

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

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

MULTIPLE POSITIVE SOLUTIONS OF INHOMOGENEOUS SEMILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS IN R~2

ＭＵＬＴＩＰＬＥＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＯＦＩＮＨＯＭＯＧＥＮＥＯＵＳＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＵＮＢＯＵＮＤＥＤＤＯＭＡＩＮＳＩＮＲ~２ＣａｏＤａｏ－Ｍｉｎ（曹道珉）（ＷｕｈａｎＩｕｓｔ．ｏｆＭｏｔｈ．Ｓｃ?..     

IR~N上拟线性椭圆型方程两解的存在性

本文证明了拟线性椭圆型方程至少有两个弱解，其中Q并且适当小．     

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

§ 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.