ESTIMATES OF EIGENVALUES FOR UNIFORMLY ELLIPTIC OPERATOR OF SECOND ORDER

ＥＳＴＩＭＡＴＥＳＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＵＮＩＦＯＲＭＬＹＥＬＬＩＰＴＩＣＯＰＥＲＡＴＯＲＯＦＳＥＣＯＮＤＯＲＤＥＲＱＩＡＮＣＨＵＮＬＩＮ（钱椿林）ＣＨＥＮＺＵＣＨＩ（陈祖墀）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｔｎａｔｉｃｓ，Ｕｎｉｖｅｒ...     

NONTRIVIAL SOLUTIONS OF THE DIRICHLET PROBLEM FOR A CLASS OF NONLINEAR ELLIPTIC EQUATIONS

Under the mild conditions by using the theory of the generalized Sobolev space and minimax theory we get the existence of solutions for a wide class of nonlinear Dirichlet problem as follows where Q is a bounded domain in . This equation is the Euler equation of the functional where     

Behaviour of solutions of the quasilinear wave equations for mechanism with a boundary piston possessing mass

1. IntroductionFor the initial-boundary Value problem of the one-dimensional quasilinear wave eqllationwhere ms r, k 2 0 are constants, there are the following known results: For m ~ r = k = 0,[1] obtained the blow-up behaviour for the solution of (1.1), and [2,3] also got the blow-upbehaviour when m = r = 0, k > 0 and m >> 1, r,k > 0 separately. [3-5] discussed thecases of m = k = 0, r > 0 and m ~ 0, r, k > 0 respectively and obtained the existence anduniquness of the global solution.In this …     

奇异拟线性椭圆型方程的可解性

本文考虑奇异拟线性椭圆型方程在球形区域中或整个空间Ｒｎ上的可解性、首先，在对拟线性算子、非线性项以及右端项系数加以适当的条件下，得到了该问题局部解的存在唯一性；然后，导出所得到的解满足一种有序性．利用这种有序性，进一步证明了该问题在以ｋ为半径的球形区域Ｂｋ上解的存在唯一性；最后，令，便得到该问题在整个空间Ｒｎ上的整体解的存在唯一性