Another look at planar Schrödinger-Newton systems

DOI10.1016/J.JDE.2022.04.035zbMath1491.35175OpenAlexW4229016437MaRDI QIDQ2139617

Chun-Lei Tang, Zhisu Liu, Vicenţiu D. Rădulescu, Jian Jun Zhang

Publication date: 18 May 2022

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

Full work available at URL: https://doi.org/10.1016/j.jde.2022.04.035

zbMATH Keywords

variational methodsconcentration-compactness principlenew perturbation approachplanar Schrödinger-Newton system

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47)

Related Items (9)

Critical Schrödinger-Bopp-Podolsky system with prescribed mass ⋮ Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case ⋮ Positive solutions to the planar logarithmic Choquard equation with exponential nonlinearity ⋮ Sufficient and necessary conditions for normalized solutions to a Choquard equation ⋮ Existence and concentration behavior of positive solutions to Schrödinger-Poisson-Slater equations ⋮ Multibump positive solutions for Choquard equation with double potentials in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ ⋮ A planar Schrödinger-Newton system with Trudinger-Moser critical growth ⋮ Groundstate for the Schrödinger-Poisson-Slater equation involving the Coulomb-Sobolev critical exponent ⋮ Positive solutions for a planar Schrödinger-Poisson system with prescribed mass

Cites Work

• Unnamed Item
• Stationary solutions of the Schrödinger-Newton model -- an ODE approach.
• Nonlinear scalar field equations. I: Existence of a ground state
• Classification of positive solitary solutions of the nonlinear Choquard equation
• On the planar Schrödinger-Poisson system
• Ground state solutions for the nonlinear Schrödinger-Maxwell equations
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• The Thomas-Fermi theory of atoms, molecules and solids
• An eigenvalue problem for the Schrödinger-Maxwell equations
• Existence and nonexistence of positive solutions for a static Schrödinger-Poisson-Slater equation
• Convergence from power-law to logarithm-law in nonlinear scalar field equations
• Solutions of Hartree-Fock equations for Coulomb systems
• On gravity's role in quantum state reduction
• Minimax theorems
• Multiplicity and concentration of positive solutions for the Schrödinger-Poisson equations
• On a logarithmic Hartree equation
• On ground state solutions for the Schrödinger-Poisson equations with critical growth
• Existence and symmetry of solutions to 2-D Schrödinger-Newton equations
• Schrödinger-Newton equations in dimension two via a Pohozaev-Trudinger log-weighted inequality
• Axially symmetric solutions for the planar Schrödinger-Poisson system with critical exponential growth
• On a planar non-autonomous Schrödinger-Poisson system involving exponential critical growth
• Ground state solutions of Nehari-Pohozaev type for the planar Schrödinger-Poisson system with general nonlinearity
• Existence of ground state solutions for the planar axially symmetric Schrödinger-Poisson system
• On the planar Schrödinger-Poisson system with the axially symmetric potential
• Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension
• Positive solution for a nonlinear stationary Schrödinger-Poisson system in \(\mathbb R^3\)
• The Schrödinger-Poisson equation under the effect of a nonlinear local term
• Positive bound state solutions for some Schrödinger–Poisson systems
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• INFINITELY MANY POSITIVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER–POISSON SYSTEM
• MULTIPLE BOUND STATES FOR THE SCHRÖDINGER–POISSON PROBLEM
• Quantum computation, entanglement and state reduction
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• Existence of positive solution for a planar Schrödinger-Poisson system with exponential growth
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• The planar Schrödinger–Poisson system with a positive potential^*
• The sign-changing solutions and ground states for planar Schrödinger–Newton system with an exponential critical growth
• Ground states and high energy solutions of the planar Schrödinger–Poisson system
• Classification of solutions for an integral equation
• On Bound States Concentrating on Spheres for the Maxwell--Schrödinger Equation
• On a class of nonlinear Schrödinger equations in \(\mathbb R^2\) involving critical growth

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