Concentrating standing waves for the fractional Schrödinger equation with critical nonlinearities

DOI10.1186/s13661-015-0507-1zbMath1333.35223OpenAlexW2255230720WikidataQ59435825 ScholiaQ59435825MaRDI QIDQ903987

Suhong Li, Yu Chen, Yanheng Ding

Publication date: 15 January 2016

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-015-0507-1

zbMATH Keywords

ground statestanding wavesconcentrationnonlocal

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) PDEs in connection with quantum mechanics (35Q40) Fractional partial differential equations (35R11)

Related Items

The concentration behavior of ground state solutions for a fractional Schrödinger-Poisson system, Ground state solutions of Schrödinger system with fractional \(p\)-Laplacian, Analysis of the damped nonlinear space-fractional Schrödinger equation, On concentration of positive ground states for the asymptotically linear fractional Schrödinger equation, Concentration-compactness for singular nonlocal Schrödinger equations with oscillatory nonlinearities, Semiclassical states for fractional Schrödinger equations with critical growth, Semiclassical states for weakly coupled fractional Schrödinger systems, Time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by Gaussian white noise, Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise

Cites Work

• Unnamed Item
• Concentration phenomenon for fractional nonlinear Schrödinger equations
• Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum
• On a class of nonlinear Schrödinger equations
• Semi-classical states for nonlinear Schrödinger equations
• Semiclassical states of nonlinear Schrödinger equations
• Multi-peak bound states for nonlinear Schrödinger equations
• Fractional quantum mechanics and Lévy path integrals
• On concentration of positive bound states of nonlinear Schrödinger equations
• Semi-classical states of nonlinear Schrödinger equations: a variational reduction method
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities
• Concentrating standing waves for the fractional nonlinear Schrödinger equation
• Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian
• A concave—convex elliptic problem involving the fractional Laplacian
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Some Theorems on Stable Processes
• Concentration on curves for nonlinear Schrödinger Equations
• OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS
• The local regularity of solutions of degenerate elliptic equations
• Existence of multi-bumb solutions for nonlinear schrödinger equations via variational method
• Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb {R}^N$RN
• An Extension Problem Related to the Fractional Laplacian