On the Kirchhoff type equations in ${\mathbb{R}}^N$

Juntao Sun, Tsung-Fang Wu

Consider a nonlinear Kirchhoff type equation as follows \begin{equation*} \left\{ \begin{array}{ll} -\left( a\int_{\mathbb{R}^{N}}|\nabla u|^{2}dx+b\right) Δu+u=f(x)\left\vert u\ri…