Multiple solutions for pp-Kirchhoff equations in RNRN

In this paper, we prove the existence of multiple ground-state solutions for the nonhomogeneous pp-Kirchhoff elliptic equation equation(0.1)M(∫RN(|∇u|p+V(x)|u|p)dx)(−Δpu+V(x)|u|p−2u)=f(x,u)+g(x),inRN, where V(x)∈C(RN)V(x)∈C(RN) and V(x)→+∞V(x)→+∞ as |x|→+∞|x|→+∞. The nonlinear function f(x,u)f(x,u) is continuous and satisfies some conditions. The solutions will be obtained by the Mountain Pass Theorem, Ekeland’s variational principle and Krasnoselskii’s genus theory in Struwe (2000) [1].