Multiplicity and concentration results for local and fractional NLS equations with critical growth
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Publication:2061735
zbMath1487.35034arXiv2101.00448MaRDI QIDQ2061735
Publication date: 21 December 2021
Published in: Advances in Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.00448
Variational methods involving nonlinear operators (47J30) Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Critical exponents in context of PDEs (35B33) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11)
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On fractional Schrödinger equations with Hartree type nonlinearities, Multiplicity of semiclassical states solutions for a weakly coupled Schrödinger system with critical growth in divergent form, Semiclassical states to the nonlinear Choquard equation with critical growth
Cites Work
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- A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in \(\mathbb{R}^N\)
- Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential
- Hitchhiker's guide to the fractional Sobolev spaces
- Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities
- Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
- Nonlinear scalar field equations. I: Existence of a ground state
- The effect of the domain's configuration space on the number of nodal solutions of singularly perturbed elliptic equations
- Symétrie et compacité dans les espaces de Sobolev
- On a class of nonlinear Schrödinger equations
- On the effect of domain topology in a singular perturbation problem
- Topological methods for variational problems with symmetries
- Semiclassical states of nonlinear Schrödinger equations
- Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations
- Fractional quantum mechanics and Lévy path integrals
- Soliton dynamics in a potential
- Dispersion managed solitons in the presence of saturated nonlinearity
- Infinite dimensional Morse theory and multiple solution problems
- On concentration of positive bound states of nonlinear Schrödinger equations
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- Local mountain passes for semilinear elliptic problems in unbounded domains
- Singularly perturbed nonlinear Dirichlet problems involving critical growth
- Necklace beams carrying fractional angular momentum in fractional systems with a saturable nonlinearity
- Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity
- On the dynamics of solitons in the nonlinear Schrödinger equation
- Concentrating solutions for a class of nonlinear fractional Schrödinger equations in \(\mathbb{R}^N\)
- Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well
- Concentrating standing waves for the fractional nonlinear Schrödinger equation
- Long time motion of NLS solitary waves in a confining potential
- Solitary wave dynamics in an external potential
- Existence and concentration of solution for a class of fractional elliptic equation in \(\mathbb {R}^N\) via penalization method
- Standing waves for nonlinear Schrödinger equations with a general nonlinearity
- On the fractional NLS equation and the effects of the potential Well's topology
- Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity
- Soliton dynamics for fractional Schrödinger equations
- Standing waves for nonlinear Schrödinger equations involving critical growth
- Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
- A BERESTYCKI–LIONS THEOREM REVISITED
- Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)a
- A remark on least energy solutions in $\mathbf {R}^N$
- Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity
- Concentration behavior of solutions for fractional Schrödinger equations involving critical exponent
- Multiple semiclassical standing waves for fractional nonlinear Schrödinger equations
- Multiple positive solutions for semilinear Schrödinger equations with critical growth in ℝN
- Ground states and concentration phenomena for the fractional Schrödinger equation
- Nonlinear scalar field equations involving the fractional Laplacian
- Existence and concentration of positive solutions for fractional nonlinear Schrödinger equation with critical growth
- Existence and concentration results for some fractional Schrödinger equations in RN with magnetic fields
- On fractional Schr$\ddot{\mbox{o}}$ödinger equation in $\mathbb {R}^{N}$RN with critical growth
- Variational Methods
- Local mountain-pass for a class of elliptic problems in \(\mathbb R^N\) involving critical growth
- Multiplicity results for some nonlinear Schrödinger equations with potentials
- Solutions concentrating around the saddle points of the potential for critical Schrödinger equations