In this paper, we study the existence of solutions to the mixed dispersion nonlinear
Schrödinger equation\[\gamma\Delta^ 2 u-\Delta u+\alpha u=| u|^{2\sigma} u,\qquad u\in H …

We study the mixed dispersion fourth order nonlinear Schrödinger equation i\partial_tψ-
γΔ^2ψ+βΔψ+|ψ|^2σψ=0\textin\mathbbR*R^N, where γ,σ>0 and β∈R. We focus on standing …

We study the focusing mass-subcritical biharmonic nonlinear Schrödinger equation (BNLS)
on the product space. Following the crucial scaling arguments introduced in [Terracini …

Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations
Page 1 Nonlinearity PAPER Dynamics of radial solutions for the focusing fourth-order …

We develop a new method, based on the Tomas-Stein inequality, to establish non-
homogeneous Gagliardo-Nirenberg-type inequalities in R N. Then we use these inequalities …

We consider ground state solutions u∈ H 2 (ℝ N) of biharmonic (fourth-order) nonlinear
Schrödinger equations of the form Δ 2 u+ 2 a Δ u+ bu−∣ u∣ p− 2 u= 0 in ℝ N with positive …

In this paper, we study the ground state standing wave solutions for the focusing bi-harmonic
nonlinear Schrödinger equation with a μ-Laplacian term (BNLS). Such BNLS models the …

We revisit the finite time blow-up for the fourth-order Schrödinger equation with focusing
inhomogeneous nonlinearity−| x|− 2| u| 4 n u. By exploiting localized virial estimates and …

Let $\gamma> 0\, $, $\beta> 0\, $, $\alpha> 0$ and $0<\sigma N< 4$. In the present paper,
we study, for $ c> 0$ given, the constrained minimization problem\begin {equation*}\label …

In this paper, we consider the strong instability of standing waves for a fourth-order nonlinear
Schrödinger equation with the mixed dispersions i ψ t− γ Δ 2 ψ+ μ Δ ψ+| ψ| p ψ= 0,(t, x)∈[0 …