Infinitely many solutions for Kirchhoff equations with indefinite potential

We obtain a sequence of solutions converging to zero for the Kirchhoff equation $$-(1+{\int }_{\mathrm{\Omega }}{\mid \mathrm{\nabla }u\mid }^2)\mathrm{\Delta }u+V(x)u=f(u)\text{,}u\in H_0^1(\mathrm{\Omega })$$ via truncating technique and a variant of Clark’s theorem due to Liu–Wang, where $\mathrm{\Omega }$ is a bounded smooth domain $\mathrm{\Omega }\subset {\mathbb{R}}^N$. Similar result for Schrödinger-Poisson system on a bounded smooth domain $\mathrm{\Omega }\subset {\mathbb{R}}^3$ is also presented.