Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity
From MaRDI portal
Publication:5357457
DOI10.1142/S0219530516500056zbMath1375.35480OpenAlexW2345769217MaRDI QIDQ5357457
Mouhamed Moustapha Fall, Yonggeun Cho, Saber Trabelsi, Hichem Hajaiej, Peter Alexander Markowich
Publication date: 8 September 2017
Published in: Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0219530516500056
Stability in context of PDEs (35B35) Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Fractional partial differential equations (35R11)
Related Items
On fractional Schrödinger equations with Hartree type nonlinearities, Existence of stable standing waves for the fractional Schrödinger equations with combined nonlinearities, On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation, On some qualitative aspects for doubly nonlocal equations, The Hartree and Hartree-Fock equations in Lebesgue \(L^p\) and Fourier-Lebesgue \(\widehat{L}^p\) spaces, Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in \(\mathbb{R}^{N}\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- A resonance problem for non-local elliptic operators
- On some critical problems for the fractional Laplacian operator
- Hitchhiker's guide to the fractional Sobolev spaces
- On blowup for time-dependent generalized Hartree-Fock equations
- The Brezis-Nirenberg type problem involving the square root of the Laplacian
- Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry
- A Harnack inequality for fractional Laplace equations with lower order terms
- Mountain pass solutions for non-local elliptic operators
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Hartree-Fock theory for pseudorelativistic atoms
- Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs
- Well-posedness for semi-relativistic Hartree equations of critical type
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
- Existence of minimizers of functionals involving the fractional gradient in the absence of compactness, symmetry and monotonicity
- Global well-posedness of critical nonlinear Schrödinger equations below \(L^2\)
- Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
- Dynamical collapse of white dwarfs in Hartree- and Hartree-Fock theory
- Fractional dynamics of systems with long-range interaction
- Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
- A concave—convex elliptic problem involving the fractional Laplacian
- On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity
- Existence and symmetry results for a Schr\"odinger type problem involving the fractional Laplacian
- Existence and stability of standing waves for nonlinear fractional Schrödinger equations
- Modeling the Cardiac Tissue Electrode Interface Using Fractional Calculus
- Regularity of the obstacle problem for a fractional power of the laplace operator
- Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
- MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE
- Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
