Orbital Stability Of Standing Waves For The Nonlinear Schr(?)dinger Equation With Hardy Potential

The aim of this dissertation is to study the orbital stability of standing waves for the following Schrodinger equation with Hardy potential and combined power nonlinearilities where N≥3,ψ0∈H1(RN),ψ:R+×RN→C,α≠0 satisfies α<α*:=((N-2)/2)2,and 2<p<2+4/N≤q<2*=2N/(N-2).In the case of q=2+4/N,by applying the method of Cazenave-Lions,we show that the set of energy minimizers is orbitally stable by studying the corresponding global minimization problem.In the case of q>2+4/N,by establishing the corresponding local minimization problem,we prove the orbital stability of the set of energy minimizers.