The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity. (Q454531)

The author proves the existence of a positive solution on \(C^2(\mathbb {R}^N)\) to the equation NEWLINE\[NEWLINE -M(\int _{\mathbb {R}^N}| \nabla u| ^2)\Delta u=g(u) NEWLINE\]NEWLINE in \(\mathbb {R}^N\), (\(N\geq 3\)) for zero-mass Berestycki-Lions nonlinearity. In the second part of the paper the existence of a ground-state solution of the above equation with \(M(s)=a+bs\), \(g(u)\) being a zero-mass Berestycki-Lions nonlinearity and \(N=3,4\), is studied.