We study the bound states to nonlinear Schrodinger equations with electro magnetic fields ihδψ/δt=（h/i -A（x））^2ψ＋V（x）ψ-K（x）｜ψ｜^p-1ψ=0,on R＋ ×R^N. Let G（x）=[V（x）p＋1/p-1-N/2][K（x）]-2/p-1 ...We study the bound states to nonlinear Schrodinger equations with electro magnetic fields ihδψ/δt=（h/i -A（x））^2ψ＋V（x）ψ-K（x）｜ψ｜^p-1ψ=0,on R＋ ×R^N. Let G（x）=[V（x）p＋1/p-1-N/2][K（x）]-2/p-1 and suppose that G（x） has k local minimum points. For h 〉 0 small, we find multi-bump bound states ~bh （x, t） ---- e-iE~/huh （X） with Uh concentrating at the local minimum points of G（x） simultaneously as h ~ O. The potentials V（x） and K（x） are allowed to be either compactly supported or unbounded at infinity.展开更多
基金supported by National Natural Science Foundation of China(11201132)Scientific Research Foundation for Ph.D of Hubei University of Technology(BSQD12065)the Scientific Research Project of Education Department of Hubei Province(Q20151401)
文摘We study the bound states to nonlinear Schrodinger equations with electro magnetic fields ihδψ/δt=（h/i -A（x））^2ψ＋V（x）ψ-K（x）｜ψ｜^p-1ψ=0,on R＋ ×R^N. Let G（x）=[V（x）p＋1/p-1-N/2][K（x）]-2/p-1 and suppose that G（x） has k local minimum points. For h 〉 0 small, we find multi-bump bound states ~bh （x, t） ---- e-iE~/huh （X） with Uh concentrating at the local minimum points of G（x） simultaneously as h ~ O. The potentials V（x） and K（x） are allowed to be either compactly supported or unbounded at infinity.
