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

DOI10.1088/1361-6544/acb62dOpenAlexW4319316154MaRDI QIDQ5874033

Pietro D'Avenia, Jacopo Schino, Alessio Pomponio

Publication date: 10 February 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.02823

zbMATH Keywords

existencenonlinear Schrödinger equationvariational methodsbi-Laplacianfourth-order dispersion term

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Higher-order elliptic equations (35J30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Cites Work

• Unnamed Item
• Unnamed Item
• Existence and multiplicity of nontrivial solutions for some biharmonic equations with \(p\)-Laplacian
• Existence and multiplicity of solutions for a class of fourth-order elliptic equations in \(R^N\)
• High energy solutions and nontrivial solutions for fourth-order elliptic equations
• The principle of symmetric criticality
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Symétrie et compacité dans les espaces de Sobolev
• Existence of solitary waves in higher dimensions
• Infinitely many nonradial solutions of a Euclidean scalar field equation
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• \(N\)-Laplacian equations in \(\mathbb{R}^N\) with critical growth
• Minimax theorems
• Adams' inequality and limiting Sobolev embeddings into Zygmund spaces
• Nonlinear scalar field equations in \(\mathbb{R}^N\): Mountain pass and symmetric mountain pass approaches
• Schrödinger equations in \(\mathbb{R}^4\) involving the biharmonic operator with critical exponential growth
• Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions
• Non-homogeneous Gagliardo-Nirenberg inequalities in \(\mathbb{R}^N\) and application to a biharmonic non-linear Schrödinger equation
• A note on deformation argument for \(L^2\) normalized solutions of nonlinear Schrödinger equations and systems
• Existence and multiplicity of solutions for fourth-order elliptic equations in \(\mathbb R^N\)
• Infinitely many solutions for fourth-order elliptic equations with general potentials
• Nonlinear scalar field equations with \(L^2\) constraint: mountain pass and symmetric mountain pass approaches
• Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case
• General class of optimal Sobolev inequalities and nonlinear scalar field equations
• Existence of solutions with prescribed norm for semilinear elliptic equations
• Self-Focusing with Fourth-Order Dispersion
• Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation
• Sharp Adams-type inequalities in ℝⁿ
• Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
• On a fourth‐order nonlinear Helmholtz equation
• Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation
• Nonradial solutions of nonlinear scalar field equations
• Nonradial normalized solutions for nonlinear scalar field equations
• 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

This page was built for publication: Radial and non-radial multiple solutions to a general mixed dispersion NLS equation