摘要：This paper is concerned with the following system: $$ \textstyle\begin{cases} {-\Delta u+\lambda A(x) u-K(x)(2 \omega +\phi ) \phi u=f(x, u)+h(x), \quad x \in \mathbb{R}^"}, \\ {\Delta \phi =K(x)(\omega +\phi ) u^,, \quad x \in \mathbb{R}^"}, \end{cases} $$ where $\lambda \geq 1$ is a parameter, $\omega >0$ is a constant and the potential A is sign-changing. Under the classic Ambrosetti–Rabinowitz condition and other suitable conditions, nontrivial solutions are obtained via the linking theorem and Ekeland’s variational principle. Especially speaking, we use a super-quadratic condition to replace the 4-superlinear condition which is usually used to show the existence of nontrivial solutions in many references. Our results improve the previous results in the literature.
