Some results on Schr(o)dinger-Poisson equations

来源 :International Conference on Variational Methods(ICAM-3)(2012 | 被引量 : 0次 | 上传用户:lianghaiyanps3
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  In this talk,I will talk about some results (joint with Dr.Z.P.Wang and Y.S.Jiang) on the following type of Schr(o)dinger-Poisson equations (SP){-△u + V (x)u + λφ (x)u = f(x,u),x ∈ R3,λ△φ = u2,x ∈ R3,where λ > 0 is a parameter,V (x) is a potential function,f(x,u) maybe the power type |u|p-1u with p ∈ (1,5) or certain general functions.The existence and properties for solutions of the problem (SP) will be discussed under different conditions on the potential V (x) and the nonlinear term f(x,u).Work supported by NSFC.
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  We consider the following classical nonlinear field equation △u - u + |u|p-1u = 0,u ∈ H1(RN),1 < p
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