摘要：The paper deals with the following Kirchhoff–Poisson systems: 0.1 $$ \textstyle\begin{cases} - ( {1+b\int _{{\mathbb{R}}^{3}} { \vert \nabla u \vert ^{2}\,dx} } ) \Delta u+u+k(x)\phi u+\lambda \vert u \vert ^{p-2}u=h(x) \vert u \vert ^{q-2}u, & x\in {\mathbb{R}}^{3}, \\ -\Delta \phi =k(x)u^{2}, & x\in {\mathbb{R}}^{3}, \end{cases} $$ where the functions k and h are nonnegative, $0\le \lambda , b$ ; $2\le p\le 4< q<6$ . Via a constraint variational method combined with a quantitative lemma, some existence results on one least energy sign-changing solution with two nodal domains to the above systems are obtained. Moreover, the convergence property of $u_{b}$ as $b \searrow 0$ is established.
关键词：Kirchhoff;Poisson systems; Least energy sign-changing solutions;
Constraint variational method; Nodal domains
