Schrödinger equation in dimension two with competing logarithmic self-interaction

Antonio Azzollini, Pietro d'Avenia, Alessio Pomponio

In this paper we study the equation \[ -Δu +(\log |\cdot|*|u|^2)u=(\log|\cdot|*|u|^q)|u|^{q-2}u, \qquad \hbox{ in }\mathbb{R}^2, \] where $8/3<q<4$. By means of variational ar…