Existence of multiple positive solutions to nonhomogeneous Schrödinger–Poisson system

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In this paper, we consider the existence of multiple solutions to the following nonhomogeneous generalized Schrödinger–Poisson system-Δu+Ku+qϕf(u)=g(u)+h(x),inR3,-Δϕ=2qF(u),inR3,where q⩾0is a parameter, 0≠h(x)=h(|x|)∈L2(R3), and g is asymptotically linear or superliner at infinity. We show that there exists q0>0 such that the system has at least two positive radial solutions for q∈[0,q0).

论文关键词:Schrödinger–Poisson system,Multiple solutions,Variational method,Cut-off function,Pohozaev identity

论文评审过程:Available online 16 March 2015.

论文官网地址:https://doi.org/10.1016/j.amc.2015.02.044