Abstract
We study a class of stationary quantum Zakharov systems with a perturbation as follows Δ2u−Δu+λV(x)u=uϕ+μf(x)|u|p−2uin R3,−Δϕ+ϕ=u2,in R3,where λ>0, μ∈R, p>1, and both f(x) and V(x) are nonnegative functions. By using the Nehari manifold, we prove the nonexistence, existence and multiplicity of nontrivial solutions, depending on the parameters λ,μ and p.
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