Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

DOI10.1088/1361-6544/ac0166zbMath1472.35351arXiv2103.10747OpenAlexW3138958576MaRDI QIDQ4997253

Marco Gallo, Silvia Cingolani, Kazunaga Tanaka

Publication date: 28 June 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.10747

zbMATH Keywords

Lagrange multipliernonlinear Schrödinger equationradially symmetric solutionfractional LaplacianPohozaev identityprescribed massnormalized solution

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal diffusion and applications
• Hitchhiker's guide to the fractional Sobolev spaces
• Nonlinear fractional Schrödinger equations in one dimension
• Corrigendum to ``The splitting lemmas for nonsmooth functionals of Hilbert spaces. II: The case at infinity
• Existence of solutions of scalar field equations with fractional operator
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear scalar field equations. I: Existence of a ground state
• Symmetry and monotonicity of least energy solutions
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Symétrie et compacité dans les espaces de Sobolev
• Fractional quantum mechanics and Lévy path integrals
• Dispersion managed solitons in the presence of saturated nonlinearity
• On the continuum limit for discrete NLS with long-range lattice interactions
• Normalized solutions of nonlinear Schrödinger equations
• Weakly coupled nonlinear Schrödinger systems: the saturation effect
• Necklace beams carrying fractional angular momentum in fractional systems with a saturable nonlinearity
• Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity
• A note on deformation argument for \(L^2\) normalized solutions of nonlinear Schrödinger equations and systems
• The numerical study for the ground and excited states of fractional Bose-Einstein condensates
• Dual variational methods in critical point theory and applications
• Nonlinear scalar field equations with \(L^2\) constraint: mountain pass and symmetric mountain pass approaches
• Erratum to: ``Existence of solutions of scalar field equations with fractional operator
• Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term
• Boson stars as solitary waves
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Existence of solutions with prescribed norm for semilinear elliptic equations
• Sharp Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces
• The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
• A remark on least energy solutions in $\mathbf {R}^N$
• Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity
• SOBOLEV INEQUALITIES WITH SYMMETRY
• Nonlinear scalar field equations involving the fractional Laplacian
• Numerical study of fractional nonlinear Schrödinger equations
• Computing the Ground and First Excited States of the Fractional Schrödinger Equation in an Infinite Potential Well