R^N上次临界带约束的极大值问题

Constrained Maximization Problem with Subcritical Sobolev Exponent in R^N

利用平移的方法解决了极大值问题S:=sup{∫RN|u|pdx;u∈H1(RN),∫RN(| u|2+u2)dx=1}的可达性,并且得到了半线性椭圆方程-△u+u=|u|p-2u,u∈H1(RN),2<p<2*的最小能量解.为了解决上述极大值问题,建立了一个集中紧性原理,而且利用这一原理,也得到了该方程的最小能量解.

Devoted to consider the constrained maximization problem:  S:=sup｛∫RN｜u｜pdx;u∈H1(RN),∫RN (｜u｜2+u2)dx=1｝.By a traslation method, can show the result of existence of maximizer of the problem. Meanwhile,obtain the result of existence of ground state solution of the following semilinear elliptic equation:-△u+u=｜u｜p-2u ,u∈H1(RN) , 2<p<2*. One the other hand, in order to solve the constrained maximization problem, construct a concentrationcompactness principle.Applying the principle,also get the result of existence of ground state solution of the above eqation.