Normalized Solutions for Lower Critical Choquard Equations with Critical Sobolev Perturbation

DOI10.1137/21M1463136zbMath1497.35145OpenAlexW4283318846MaRDI QIDQ5092874

No author found.

Publication date: 26 July 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/21m1463136

zbMATH Keywords

critical exponentsvariational methodnormalized solutionsChoquard equations

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items

Critical Schrödinger-Bopp-Podolsky system with prescribed mass ⋮ Normalized solutions for the fractional Choquard equations with Hardy-Littlewood-Sobolev upper critical exponent ⋮ Normalized solutions to the critical Choquard-type equations with weakly attractive potential and nonlocal perturbation ⋮ Supersolutions to nonautonomous Choquard equations in general domains ⋮ Normalized solutions for a Choquard equation with exponential growth in \(\mathbb{R}^2\) ⋮ Ground states for nonlinear fractional Schrödinger–Poisson systems with general convolution nonlinearities ⋮ Normalized solutions of nonhomogeneous mass supercritical Schrödinger equations in bounded domains ⋮ Normalized ground states for the lower critical fractional Choquard equation with a focusing local perturbation ⋮ Normalized bound states for the Choquard equations in exterior domains ⋮ Sufficient and necessary conditions for normalized solutions to a Choquard equation ⋮ Existence and asymptotics of normalized ground states for a Sobolev critical Kirchhoff equation ⋮ Multibump positive solutions for Choquard equation with double potentials in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ ⋮ Multiplicity and concentration of positive solutions for critical Choquard equations with concave perturbation ⋮ Normalized solutions to lower critical Choquard equation with a local perturbation ⋮ Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent ⋮ Normalized solutions for the \(p\)-Laplacian equation with a trapping potential ⋮ Normalized solutions to fractional mass supercritical NLS systems with Sobolev critical nonlinearities ⋮ Positive solutions for a planar Schrödinger-Poisson system with prescribed mass

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A guide to the Choquard equation
• A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems
• On a periodic Schrödinger equation with nonlocal superlinear part
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Best constant in Sobolev inequality
• The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
• Minimax theorems
• Existence of normalized ground states for the Sobolev critical Schrödinger equation with combined nonlinearities
• Standing waves to upper critical Choquard equation with a local perturbation: multiplicity, qualitative properties and stability
• Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
• Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case
• Normalized ground states for the NLS equation with combined nonlinearities
• Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
• Derivation of Hartree's theory for generic mean-field Bose systems
• Multi-bump solutions for Choquard equation with deepening potential well
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• The existence of positive solutions with prescribed L2-norm for nonlinear Choquard equations
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Mean field dynamics of boson stars
• Quantum computation, entanglement and state reduction
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• The Schrödinger–Newton equation as a non-relativistic limit of self-gravitating Klein–Gordon and Dirac fields
• Choquard equations with critical nonlinearities
• Nehari‐type ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation
• Stationary Waves with Prescribed $L^2$-Norm for the Planar Schrödinger--Poisson System
• Nonexistence, existence and symmetry of normalized ground states to Choquard equations with a local perturbation