Existence and concentration of ground state solution to a nonlocal Schrödinger equation

DOI10.1063/5.0008911zbMath1452.81101OpenAlexW3036799717MaRDI QIDQ5136142

Qian Zhang, Anmin Mao

Publication date: 25 November 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/5.0008911

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Critical exponents in context of PDEs (35B33) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Existence and concentration of ground state solutions for Kirchhoff type equations with general nonlinearities, Multiple positive solutions for Kirchhoff-type equations involving critical-concave nonlinearities

Cites Work

• Unnamed Item
• Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in \(\mathbb R^2\)
• Existence and concentration of solutions for the Schrödinger-Poisson equations with steep well potential
• Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth
• Ground state sign-changing solutions for a class of Schrödinger-Poisson type problems in \({\mathbb{R}^{3}}\)
• Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in \(\mathbb R^N\)
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Nontrivial solutions of Kirchhoff-type problems via the Yang index
• On the existence of solutions for the Schrödinger-Poisson equations
• Infinitely many radial solutions for Kirchhoff-type problems in \(\mathbb{R}^N\)
• Positive solutions for Schrödinger-Poisson equations with a critical exponent
• Regularity for a more general class of quasilinear equations
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• Remarks on the Schrödinger operator with singular complex potentials
• Positive solutions for a nonlinear nonlocal elliptic transmission problem
• Elliptic partial differential equations of second order
• Ground state sign-changing solutions for a Schrödinger-Poisson system with a critical nonlinearity in \(\mathbb{R}^3\)
• On the variational principle
• Minimax theorems
• Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
• Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent
• Ground state solutions for an indefinite Kirchhoff type problem with steep potential well
• Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
• The Schrödinger-Poisson equation under the effect of a nonlinear local term
• Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition
• Concentrating Bound States for Kirchhoff Type Problems in ℝ³ Involving Critical Sobolev Exponents
• On a class of nonlocal elliptic problems with critical growth
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• On harnack type inequalities and their application to quasilinear elliptic equations