Infinitely many entire solutions to a mixed dispersion Schrödinger equation with generic non-linearity.

Abstract. I will present a multiplicity result for the mixed dispersion non-linear Schrödinger equation
\[\Delta^2u−\beta \Delta u=g(u), \qquad \mbox{in}\quad\mathbb{R}^N \]

focusing on the case $N \geq 5$, where the non-linearity $g\colon\mathbb R\to \mathbb R$ satisfies assumptions in the spirit of Berestycki & Lions.After showing some compactness results, I will demonstrate how the variational approach of [1], which makes use of auxiliary functionals, can be used for this problem.

Posted on Oct 25, 2021 in Differential Equations, Seminars