Existence of Bound States for Schrödinger-Newton Type Systems

DOI10.1515/ans-2013-0214zbMath1278.35072OpenAlexW2367940332MaRDI QIDQ5299007

Giusi Vaira

Publication date: 25 June 2013

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2013-0214

zbMATH Keywords

variational methodslack of compactnessnonautonomous Schrödinger-Poisson system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Second-order elliptic systems (35J47) Positive solutions to PDEs (35B09)

Related Items (16)

High energy solutions of the Choquard equation ⋮ Existence and local uniqueness of normalized peak solutions for a Schrödinger-Newton system ⋮ Existence of positive ground state solutions for the coupled Choquard system with potential ⋮ Standing waves for a coupled nonlinear Hartree equations with nonlocal interaction ⋮ Asymptotic properties of ground states to the Choquard equation with generalized autonomous perturbation ⋮ Non-existence of multi-peak solutions to the Schrödinger-Newton system with \(L^2\)-constraint ⋮ Dichotomous concentrating solutions for a Schrödinger-Newton equation ⋮ Existence and qualitative properties of solutions for Choquard equations with a local term ⋮ Uniqueness of positive solutions with concentration for the Schrödinger-Newton problem ⋮ Multiple nodal solutions of quadratic Choquard equations with perturbation ⋮ A guide to the Choquard equation ⋮ Infinitely many bound states for Choquard equations with local nonlinearities ⋮ Non-degeneracy of peak solutions to the Schrödinger-Newton system ⋮ Multi-peak positive solutions of a nonlinear Schrödinger-Newton type system ⋮ On a class of nonlocal nonlinear Schrödinger equations with potential well ⋮ Existence and nonexistence of nodal solutions for Choquard type equations with perturbation

Cites Work

• Classification of positive solitary solutions of the nonlinear Choquard equation
• Some nonlinear elliptic problems in unbounded domains
• The effect of concentrating potentials in some singularly perturbed problems
• On the variational principle
• Uniqueness of Positive Bound States to Schrödinger Systems with Critical Exponents

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