Existence of positive ground state solutions for Kirchhoff type equation with general critical growth - Liu, Zhisu; Luo, Chaoliang (Topological Methods in Nonlinear Analysis, 2016)
We study the existence of positive ground state solutions for the nonlinear Kirchhoff type equation cases -(a+b_R^3| abla u|^2)Δ u+V(x)u =f(u) & in R^3, oalign uH^1(R^3), u> 0 & in R^3, cases % where a,b> 0 are constants, fC(R,R) has general critical growth. We generalize a Berestycki-Lions theorem about the critical case of Schrödinger equation to Kirchhoff type equation via variational methods. Moreover, some subcritical works on Kirchhoff type equation are extended to the current critical case.