Fractional Schrödinger equation; solvability and connection with classical Schrödinger equation

DOI10.1016/J.JMAA.2017.08.014OpenAlexW2748042844MaRDI QIDQ2405374

Flank D. M. Bezerra, Marcelo J. D. Nascimento, Tomasz Dlotko, Alexandre Nolasco De Carvalho

Publication date: 25 September 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.08.014

zbMATH Keywords

fractional powers of operatorsfractional Schrödinger equationsubcritical nonlinearity

Mathematics Subject Classification ID

Ordinary differential equations (34-XX) Partial differential equations (35-XX)

Related Items (13)

Long-time dynamics for a fractional piezoelectric system with magnetic effects and Fourier's law ⋮ Logarithmic counterpart for semilinear Schrödinger equations ⋮ Fractional powers approach of operators for abstract evolution equations of third order in time ⋮ Global existence and convergence results for a class of nonlinear time fractional diffusion equation ⋮ On the limit of solutions for a reaction-diffusion equation containing fractional Laplacians ⋮ Long-time behavior for evolution processes associated with non-autonomous nonlinear Schrödinger equation ⋮ Fractional approximations of abstract semilinear parabolic problems ⋮ Random flights connecting porous medium and Euler–Poisson–Darboux equations ⋮ On a cascade system of Schrödinger equations. Fractional powers approach ⋮ Finite dimensionality of the global attractor for a fractional Schrödinger equation on \(\mathbb{R}\) ⋮ Existence and upper-semicontinuity of global attractors for binary mixtures solids with fractional damping ⋮ Quasi-stability and continuity of attractors for nonlinear system of wave equations ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The generalized Korteweg-de Vries-Burgers equation in \(H^2(\mathbb R)\)
• Uniform decay rates for the energy of weakly damped defocusing semilinear Schrödinger equations with inhomogeneous Dirichlet boundary control
• Global attractor and asymptotic smoothing effects for the weakly damped cubic Schrödinger equation in \(L^2(\mathbb{T})\)
• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• Global attractor for weakly damped nonlinear Schrödinger equations in \(L^2(\mathbb R)\)
• Semigroups of linear operators and applications to partial differential equations
• Unified theory for abstract parabolic boundary problems - a semigroup approach
• Geometric theory of semilinear parabolic equations
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• Parabolic problems with nonlinear boundary conditions and critical nonlinearities
• Infinite-dimensional dynamical systems in mechanics and physics.
• Product rule and chain rule estimates for fractional derivatives on spaces that satisfy the doubling condition
• Fractional powers of operators. II: Interpolation spaces
• Principles of Fractional Quantum Mechanics
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Abstract Parabolic Evolution Equations and their Applications
• Fractional powers of operators

This page was built for publication: Fractional Schrödinger equation; solvability and connection with classical Schrödinger equation