H^1(R^N)上一类带限制的Schrdinger方程的正负解

Positive and Negative Solutions of a Schrdinger Equation with Constraint in H^1(R^N)

应用变分方法,以拓扑度理论为依据,研究H^1(R^N)空间上一类带限制的半线性Schrdinger方程。通过构造适当的伪梯度向量场,解决带限制的半线性Schrdinger方程的Cauchy问题,证明其在周期和适当限制条件下解的存在性,并获得带限制的半线性椭圆特征问题的一个正解与一个负解。

Based on topology degree theory,variational method was applied to research a class of semilinear Schrodinger equation in H^1( R^N) with constraint in this paper. By constructing pseudo-gradient vector field,the Cauchy problem was solved and the existence of solution under the periodic and appropriate condition was proved. Finally,a positive solution and a negative solution of the semilinear elliptic problem with constraint were obtained.