Normalized solutions to the Kirchhoff equation with a perturbation term. (Q2093361)

The paper deals with existence and non-existence questions related to the normalized solutions of the Kirchhoff equation \[-\Big(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\Big)\Delta u=\lambda u+|u|^{p-2}u+\mu|u|^{q-2}u\quad\text{in}\ \mathbb{R}^3,\] with prescribed mass \[\int_{\mathbb{R}^3}|u|^2dx=c,\] where \(a,b>0\), \(\mu\in\mathbb{R}\) and \(2<q<p<6\). By means of the constraint minimization and concentration compactness principle, the author obtains results on existence or non-existence of normalized solutions, partially extending already known results.