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On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system
In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system { − Δ u + V ( x ) u − ( 2 ω +… Click to show full abstract
In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system
{−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u),x∈R3,Δϕ=(ω+ϕ)u2,x∈R3, where ω>0 is a constant and the nonlinearity f(x,u) is either asymptotically linear in u at infinity or the primitive of f(x,u) is of 4-superlinear growth in u at infinity. Under some suitable assumptions, the existence and multiplicity of solutions are proved by using the Mountain Pass theorem and the fountain theorem, respectively.
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