In this paper,we study the following three-dimensional Schrodinger equation with combined Hartree-type and power-type nonlinearities i∂ψ+△ψ+(|x|^(-2)*|ψ|^(2))ψ+|ψ|^(p-1)=0 with 1<p<5.Using standard variati...In this paper,we study the following three-dimensional Schrodinger equation with combined Hartree-type and power-type nonlinearities i∂ψ+△ψ+(|x|^(-2)*|ψ|^(2))ψ+|ψ|^(p-1)=0 with 1<p<5.Using standard variational arguments,the existence of ground state solutions is obtained.And then we prove that when p≥3,the standing wave solution e^(1ωt)u_(ω)(x)is strongly unstable for the frequencyω>0.展开更多
文摘In this paper,we study the following three-dimensional Schrodinger equation with combined Hartree-type and power-type nonlinearities i∂ψ+△ψ+(|x|^(-2)*|ψ|^(2))ψ+|ψ|^(p-1)=0 with 1<p<5.Using standard variational arguments,the existence of ground state solutions is obtained.And then we prove that when p≥3,the standing wave solution e^(1ωt)u_(ω)(x)is strongly unstable for the frequencyω>0.
