Stability analysis of standing waves for nonlinear Schrodinger equations

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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