Abstract
In this paper, we prove the existence of multiple solutions for the following Klein–Gordon equation with concave and convex nonlinearities coupled with Born–Infeld theory {−Δu+a(x)u−(2ω+ϕ)ϕu=λk(x)|u|q−2u+g(x)|u|p−2u,x∈R3,Δϕ+βΔ4ϕ=4π(ω+ϕ)u2,x∈R3, where 1<q<2<p<6. Under appropriate assumptions on a, k, g and λ, the existence of multiple nontrivial solutions is proved by using the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.
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