Non-homogeneous Gagliardo-Nirenberg inequalities in \(\mathbb{R}^N\) and application to a biharmonic non-linear Schrödinger equation

DOI10.1016/j.jde.2022.04.037zbMath1491.35163arXiv2010.01448OpenAlexW4280541849MaRDI QIDQ2143957

Louis Jeanjean, Antonio J. Fernández, Mihai Mariş, Rainer Mandel

Publication date: 31 May 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.01448

zbMATH Keywords

standing wavesGagliardo-Nirenberg inequalitiesglobal and local minimizationbiharmonic non-linear Schrödinger equation with mixed dispersion

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Higher-order elliptic equations (35J30) Variational methods for higher-order elliptic equations (35J35)

Related Items (7)

Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians ⋮ Normalized solutions to biharmonic Schrödinger equation with critical growth in \(\mathbb{R}^N\) ⋮ Normalized solutions for the mixed dispersion nonlinear Schrödinger equations with four types of potentials and mass subcritical growth ⋮ Existence and multiplicity of normalized solutions to biharmonic Schrödinger equations with subcritical growth ⋮ Normalized ground states of nonlinear biharmonic Schrödinger equations with Sobolev critical growth and combined nonlinearities ⋮ On global minimizers for a mass constrained problem ⋮ Radial and non-radial multiple solutions to a general mixed dispersion NLS equation

Cites Work

• Unnamed Item
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• On the lowest eigenvalue of the Laplacian for the intersection of two domains
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Functional analysis, Sobolev spaces and partial differential equations
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• Scattering theory for the fourth-order Schrödinger equation in low dimensions
• Self-Focusing with Fourth-Order Dispersion
• Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity
• Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation
• Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
• On symmetry of traveling solitary waves for dispersion generalized NLS
• Blowup for Biharmonic NLS
• Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion
• Strong Instability of Ground States to a Fourth Order Schrödinger Equation

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