Stability analysis of standing waves for nonlinear Schrodinger equations

在2011学年，我学习了两种科目。第一个是关于带调和势的非线性椭圆型方程的奇异解。在这里，我们考虑的纯幂非线性与Sobolev超临界指数。在2012学年，我们研究了具有一般非线性项的非线性薛定谔方程的散射问题。在这里，我们引入了与方程相关联的某个泛函，并假设非线性度满足

In the academic year of 2011, I studied two kinds of subjects. One is concerned with a singular solution to nonlinear elliptic equations with the harmonic potential. Here, we consider the pure power nonlinearity with the Sobolev supercritical exponent. ThIn the academic year of 2012, we studied the scattering problem for the nonlinear Schrodinger equations with general nonlinearities. Here, we introduced a certain functional associated with the equations and assumed the nonlinearities satisfy the value of