| 1 | Multiple solutions for a Schrdinger-Poisson-Slater equation with external Coulomb potential显示文摘Consider the following Schrdinger-Poisson-Slater system,(P)u+ω-β|x|u+λφ(x)u=|u|p-1u,x∈R3,-φ=u2,u∈H1(R3),whereω>0,λ>0 andβ>0 are real numbers,p∈(1,2).Forβ=0,it is known that problem(P)has no nontrivial solution ifλ>0 suitably large.Whenβ>0,-β/|x|is an important potential in physics,which is called external Coulomb potential.In this paper,we find that(P)withβ>0 has totally different properties from that ofβ=0.Forβ>0,we prove that(P)has a ground state and multiple solutions ifλ>cp,ω,where cp,ω>0 is a constant which can be expressed explicitly viaωand p. | JIANG YongSheng ZHOU HuanSong | 2014 | Science China Mathematics2014，57，6： | 5 |
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