Radial and non-radial multiple solutions to a general mixed dispersion NLS equation

Abstract

We study the following nonlinear Schrödinger equation with a forth order dispersion term \[ Δ^2u-βΔu=g(u) \quad \text{in } \mathbb{R}^N \] in the positive and zero mass regimes: in the former, $N\ge 2$ and $\beta >-2\sqrt{m}$, where $m>0$ depends on $g$; in the latter, $N\ge 3$ and $\beta >0$. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about $g$; if $N=2$ in the positive mass case, or $N=4$ in the zero mass case, we need to strengthen such assumptions. Our approach is variational.

arXiv comment28 pages, revised version

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Cited by in corpus (1)

• Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation