This paper is devoted to dealing with the following nonlinear Kirchhoff type problem with general convolution nonlinearity and variable potential: $$\left\{\begin{array}{ll} -({a + b\int_{{\R^3}} | \nabla u{|^2}dx})\Delta u + V(x)u =(I_{\alpha}\ast F(u))f(u),\quad \text{in}\ \ \R^3,\\ u \in H^{1} (\R^{3}), \end{array}\right.$$ where $a>0$, $b\geq0$ are constants, $V\in C^1(\R^3,[0,+\infty))$, $f\in C(\R,\R)$, $F(t)=\int_{0}^{t}f(s)ds$, $I_{\alpha}:\R^{3}\rightarrow \R$ is the Riesz potential, $\alpha\in(0,3)$. By applying some new analytical tricks introduced by [X.H. Tang, S.T. Chen, Adv. Nonlinear Anal. 9 (2020) 413-437], the existence results of ground state solutions of Poho\v{z}aev type for the above Kirchhoff type problem are obtained under some mild assumptions on $V$ and the general “Berestycki-Lions assumptions” on the nonlinearity $f$. Our results generalize and improve the ones in [P. Chen, X.C. Liu, J. Math. Anal. Appl. 473 (2019) 587-608.] and other related results in the literature.

This paper is devoted to dealing with the following nonlinear Kirchhoff‐type problem with general convolution nonlinearity and variable potential: {left leftarray−(a+b∫ℝ3|∇u|2dx)Δu+V(x)u=(Iα∗F(u))f(u),inℝ3,arrayu∈H1(ℝ3),$$ \left\{\begin{array}{l}-\left(a+b{\int}_{{\mathbb{R}}^3}{\left|\nabla u\right|}^2 dx\right)\Delta u+V(x)u=\left({I}_{\alpha}\ast F(u)\right)f(u),\kern0.30em \mathrm{in}\kern0.50em {\mathbb{R}}^3,\\ {}u\in {H}^1\left({\mathbb{R}}^3\right),\end{array}\right. $$ where a>0$$ a>0 $$, b≥0$$ b\ge 0 $$ are constants; V∈C1false(ℝ3,false[0,+∞false)false)$$ V\in {C}^1\left({\mathbb{R}}^3,\right[0,+\infty \left)\right) $$; f∈Cfalse(ℝ,ℝfalse)$$ f\in C\left(\mathbb{R},\mathbb{R}\right) $$, Ffalse(tfalse)=∫0tffalse(sfalse)ds$$ F(t)={\int}_0^tf(s) ds $$; and Iα:ℝ3→ℝ$$ {I}_{\alpha }:{\mathbb{R}}^3\to \mathbb{R} $$ is the Riesz potential, α∈false(0,3false)$$ \alpha \in \left(0,3\right) $$. By applying some new analytical tricks introduced by Tang and Chen, the existence results of ground state solutions of Pohožaev type for the above Kirchhoff type problem are obtained under some mild assumptions on V$$ V $$ and the general “Berestycki‐Lions assumptions” on the nonlinearity f$$ f $$. Our results generalize and improve the ones obtained by Chen and Liu and other related results in the literature.