The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a comb...The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.展开更多
Under the assumption that F is asymptotically or super linear as ｜U｜→∞ with U = （u,v）∈R^2, we obtain the existence of ground state solutions of a class of cooperative elliptic systems in NN by using a variant g...Under the assumption that F is asymptotically or super linear as ｜U｜→∞ with U = （u,v）∈R^2, we obtain the existence of ground state solutions of a class of cooperative elliptic systems in NN by using a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. To the best of our knowledge, there is no result published concerning the systems in the whole space N^N.展开更多
This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures loc...This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.展开更多
This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and th...This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.展开更多
基金Supported by National Natural Science Foundation of China (No. 10971153 and No. 10671141)
文摘The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.
基金supported by National Natural Science Foundation of China (Grant No.11171163)
文摘Under the assumption that F is asymptotically or super linear as ｜U｜→∞ with U = （u,v）∈R^2, we obtain the existence of ground state solutions of a class of cooperative elliptic systems in NN by using a variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou. To the best of our knowledge, there is no result published concerning the systems in the whole space N^N.
文摘This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.
基金supported by the National Natural Science Foundation of China(No.11171220)the Shanghai Leading Academic Discipline Project(No.XTKX2012)the Hujiang Foundation of China(No.B14005)
文摘This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.
