Semi-classical analysis around local maxima and saddle points for degenerate nonlinear Choquard equations
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Publication:6168102
DOI10.1007/s12220-023-01367-xzbMath1519.35287OpenAlexW4384821856MaRDI QIDQ6168102
Kazunaga Tanaka, Silvia Cingolani
Publication date: 8 August 2023
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s12220-023-01367-x
Variational methods applied to PDEs (35A15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
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- Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential
- Multiple solutions to a magnetic nonlinear Choquard equation
- Semiclassical states for the nonlinear Schrödinger equation on saddle points of the potential via variational methods
- Semi-classical states for the Choquard equation
- Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity
- Multiple interior and boundary peak solutions to singularly perturbed nonlinear Neumann problems under the Berestycki-Lions condition
- Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations
- A guide to the Choquard equation
- Semi-classical standing waves for nonlinear Schrödinger systems
- Multiplicity and concentration of solutions to the nonlinear magnetic Schrödinger equation
- Nonlinear scalar field equations. I: Existence of a ground state
- Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations
- Uniqueness of ground states for pseudorelativistic Hartree equations
- Classification of positive solitary solutions of the nonlinear Choquard equation
- On a class of nonlinear Schrödinger equations
- On the point-particle (Newtonian) limit of the nonlinear Hartree equation
- Semiclassical states of nonlinear Schrödinger equations
- Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations
- On a singularly perturbed elliptic equation
- On concentration of positive bound states of nonlinear Schrödinger equations
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- Semi-classical states of nonlinear Schrödinger equations: a variational reduction method
- Local mountain passes for semilinear elliptic problems in unbounded domains
- On gravity's role in quantum state reduction
- Intertwining semiclassical solutions to a Schrödinger-Newton system
- Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part
- Nonlinear scalar field equations in \(\mathbb{R}^N\): Mountain pass and symmetric mountain pass approaches
- Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
- Semiclassical states for critical Choquard equations
- Singularly perturbed critical Choquard equations
- Multi-bump standing waves for nonlinear Schrödinger equations with a general nonlinearity: the topological effect of potential wells
- Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities
- A note on deformation argument for \(L^2\) normalized solutions of nonlinear Schrödinger equations and systems
- Normalized solutions for a class of nonlinear Choquard equations
- Multi-bump positive solutions for a nonlinear elliptic problem in expanding tubular domains
- Positive and sign changing solutions to a nonlinear Choquard equation
- Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well
- Nonlinear scalar field equations with \(L^2\) constraint: mountain pass and symmetric mountain pass approaches
- Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well
- Existence and concentration for Kirchhoff type equations around topologically critical points of the potential
- Multiplicity and concentration for Kirchhoff type equations around topologically critical points in potential
- Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
- Standing waves for nonlinear Schrödinger equations with a general nonlinearity
- On the fractional NLS equation and the effects of the potential Well's topology
- Multiplicity of concentrating solutions for Choquard equation with critical growth
- Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities
- Deformation Argument under PSP Condition and Applications
- Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)a
- Quantum computation, entanglement and state reduction
- Strongly interacting bumps for the Schrödinger–Newton equations
- The Choquard equation and related questions
- Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
- Spherically-symmetric solutions of the Schrödinger-Newton equations
- A remark on least energy solutions in $\mathbf {R}^N$
- Erratum: Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation (2021 Nonlinearity 34 4017)
- Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass
- Existence of groundstates for a class of nonlinear Choquard equations
- Multi-peak solution for nonlinear magnetic Choquard type equation
- The ground state energy of the Schrödinger-Newton equation
- Multiplicity results for some nonlinear Schrödinger equations with potentials
