Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent
Lan Zeng, Chun Lei Tang · Annales Polonici Mathematici · 2016
We consider the following Kirchhoff type problem involving a critical nonlinearity: \begin{equation*} \begin{cases} \displaystyle-\bigg[a+b\bigg(\int_{\Omega}| abla u|^{2}\,dx\bigg)^{m}\bigg]\Delta u= f(x,u)+|u|^{2^{\ast}-2}u &\text{in $\Omega$,} \\ u=0