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\begin{document}

\title{Ground state solutions of Poho\textbackslash{}v\{z\}aev type for
Kirchhoff type problems with general convolution nonlinearity and
variable potential}



\author[1]{Qiongfen Zhang}%
\author[1]{Hai Xie}%
\author[1]{Yirong Jiang}%
\affil[1]{Guilin University of Technology}%


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  \date{May 27, 2024}


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\begin{abstract}
This paper is devoted to dealing with the following nonlinear Kirchhoff
type problem with general convolution nonlinearity and variable
potential:
\$\$\textbackslash{}left\textbackslash{}\{\textbackslash{}begin\{array\}\{ll\}
-(\{a + b\textbackslash{}int\_\{\{\textbackslash{}R\^{}3\}\} \textbar{}
\textbackslash{}nabla u\{\textbar{}\^{}2\}dx\})\textbackslash{}Delta u +
V(x)u =(I\_\{\textbackslash{}alpha\}\textbackslash{}ast
F(u))f(u),\textbackslash{}quad
\textbackslash{}text\{in\}\textbackslash{} \textbackslash{}
\textbackslash{}R\^{}3,\textbackslash{}\textbackslash{} u
\textbackslash{}in H\^{}\{1\} (\textbackslash{}R\^{}\{3\}),
\textbackslash{}end\{array\}\textbackslash{}right.\$\$ where
\$a\textgreater{}0\$, \$b\textbackslash{}geq0\$ are constants,
\$V\textbackslash{}in
C\^{}1(\textbackslash{}R\^{}3,{[}0,+\textbackslash{}infty))\$,
\$f\textbackslash{}in C(\textbackslash{}R,\textbackslash{}R)\$,
\$F(t)=\textbackslash{}int\_\{0\}\^{}\{t\}f(s)ds\$,
\$I\_\{\textbackslash{}alpha\}:\textbackslash{}R\^{}\{3\}\textbackslash{}rightarrow
\textbackslash{}R\$ is the Riesz potential,
\$\textbackslash{}alpha\textbackslash{}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\textbackslash{}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.%
\end{abstract}%



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