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In this article, we study two classes of Kirchhoff-type equations as follows:−a+b∫R3∣∇u∣2dxΔu+V(x)u=(Iα∗∣u∣p)∣u∣p−2u+f(u),inR3,u∈H1(R3),\left\{\begin{array}{l}-\left(a+b\underset{{{\mathbb{R}}}^{3}}{\overset{}{\int }}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+V\left(x)u=({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u+f\left(u),\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3},\\ u\in {H}^{1}\left({{\mathbb{R}}}^{3}),\end{array}\right.\hspace{1.85em}and−a+b∫R3∣∇u∣2dxΔu+V(x)u=(Iα∗∣u∣p)∣u∣p−2u+m∣u∣l−2u,inR3,u∈H1(R3),\left\{\begin{array}{l}-\left(a+b\underset{{{\mathbb{R}}}^{3}}{\overset{}{\int }}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+V\left(x)u=({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u+m| u{| }^{l-2}u,\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3},\\ u\in {H}^{1}\left({{\mathbb{R}}}^{3}),\end{array}\right.wherea&gt;0a\gt 0,b≥0b\ge 0,α∈(0,3)\alpha \in \left(0,3),(3+α)/3&lt;p&lt;(3+α)\left(3+\alpha )\hspace{0.1em}\text{/}\hspace{0.1em}3\lt p\lt \left(3+\alpha ),l≥6l\ge 6,m&gt;0m\gt 0,V:R3→RV:{{\mathbb{R}}}^{3}\to {\mathbb{R}}is a potential function andIα{I}_{\alpha }is a Riesz potential whose order isα∈(0,3)\alpha \in \left(0,3). Under some assumptions onV(x)V\left(x)andf(u)f\left(u), we can prove that the equations have ground state solutions by variational methods.

Ground state solution for some new Kirchhoff-type equations with Hartree-type nonlinearities and critical or supercritical growth