The existence of generalized solution to the initial value problem iu_t+△u+k/(x_N)u_X_N+q(x)u+|u|^(p-1)u=0 on R^N is studied, By Galerkin method, we prove that the solution always exists for every initial value in H^...The existence of generalized solution to the initial value problem iu_t+△u+k/(x_N)u_X_N+q(x)u+|u|^(p-1)u=0 on R^N is studied, By Galerkin method, we prove that the solution always exists for every initial value in H^1(R^N; k) if 1<p<(N+k)/(N+k-2), N≥2. Finally, we prove orbital stability of standing waves for nonlinear singular Schr(?)dinger equation.展开更多
This paper is concerned with the existence of nontrivial solutions of the somilinear olliptio equations on unbounded domain Ω in R~n, N≥2. These results extend Rose of [11], [13] and [16]. The main tool is variation...This paper is concerned with the existence of nontrivial solutions of the somilinear olliptio equations on unbounded domain Ω in R~n, N≥2. These results extend Rose of [11], [13] and [16]. The main tool is variational methods in this paper.展开更多
The day of May 12, 1989 is the 70 th birthday of Professor Wu Wen-tsn, an outstanding Ghinese mathematician, an internationally recognized topologist and a founder of Mechanized Mathematic. After long years of arduous...The day of May 12, 1989 is the 70 th birthday of Professor Wu Wen-tsn, an outstanding Ghinese mathematician, an internationally recognized topologist and a founder of Mechanized Mathematic. After long years of arduous research endeavors, Wu has made enormous achievements in various aspects, and won for himself an international reputation. Wu Wen-tsn was fomerly deputy direcor of Institute of Mathematies, Academia Sinica and then deputy directer of Institute of Systems Sciences, Acade-展开更多
The present paper gives several theorems concerning analytic and harmonic continuations described by distributional limits. For distributions on spheres, comparatively complete results are given. Generalizing the Dire...The present paper gives several theorems concerning analytic and harmonic continuations described by distributional limits. For distributions on spheres, comparatively complete results are given. Generalizing the Direchlet and Neumann problem so that the boundary values are distributions, we obtain the results on existence and uniqueness. For one complex variable, a generalized Riemann's mapping theorem is obtained.展开更多
文摘The existence of generalized solution to the initial value problem iu_t+△u+k/(x_N)u_X_N+q(x)u+|u|^(p-1)u=0 on R^N is studied, By Galerkin method, we prove that the solution always exists for every initial value in H^1(R^N; k) if 1<p<(N+k)/(N+k-2), N≥2. Finally, we prove orbital stability of standing waves for nonlinear singular Schr(?)dinger equation.
文摘This paper is concerned with the existence of nontrivial solutions of the somilinear olliptio equations on unbounded domain Ω in R~n, N≥2. These results extend Rose of [11], [13] and [16]. The main tool is variational methods in this paper.
文摘The day of May 12, 1989 is the 70 th birthday of Professor Wu Wen-tsn, an outstanding Ghinese mathematician, an internationally recognized topologist and a founder of Mechanized Mathematic. After long years of arduous research endeavors, Wu has made enormous achievements in various aspects, and won for himself an international reputation. Wu Wen-tsn was fomerly deputy direcor of Institute of Mathematies, Academia Sinica and then deputy directer of Institute of Systems Sciences, Acade-
文摘The present paper gives several theorems concerning analytic and harmonic continuations described by distributional limits. For distributions on spheres, comparatively complete results are given. Generalizing the Direchlet and Neumann problem so that the boundary values are distributions, we obtain the results on existence and uniqueness. For one complex variable, a generalized Riemann's mapping theorem is obtained.
