Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
Reads0
Chats0
TLDR
In this article, the existence of positive solutions for the nonlinear Schrodinger equation with the fractional Laplacian was studied and the regularity, decay and symmetry properties of these solutions were analyzed.Abstract:
We study the existence of positive solutions for the nonlinear Schrodinger equation with the fractional LaplacianFurthermore, we analyse the regularity, decay and symmetry properties of these solutions.read more
Citations
More filters
Journal ArticleDOI
Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
TL;DR: In this paper, the authors considered a semilinear elliptic problem and proved the existence of a positive groundstate solution of the Choquard or nonlinear Schr\"odinger--Newton equation for an optimal range of parameters.
Journal ArticleDOI
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p -Laplacian in $${\mathbb {R}}^N$$ R N
TL;DR: In this article, the existence of multiple solutions for the nonhomogeneous fractional p-Laplacian equations of Schrodinger-Kirchhoff type was investigated, and multiplicity results were obtained by using the Ekeland variational principle and the Mountain Pass theorem.
Journal ArticleDOI
Concentrating standing waves for the fractional nonlinear Schrödinger equation
TL;DR: In this article, the authors considered the semilinear equation e 2 s ( − Δ ) s u + V ( x ) u − u p = 0, u > 0, u ∈ H 2 s n (R N ) where 0 s 1, 1 p N + 2 s N − 2 s, V (x ) is a sufficiently smooth potential with inf R V(x ) > 0, and e > 0 is a small number.
Journal ArticleDOI
Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity
TL;DR: In this article, a scalar field equation involving a fractional Laplacian was studied and a positive ground state was obtained under the general Berestycki-Lions type assumptions.
Journal ArticleDOI
Elliptic problems involving the fractional Laplacian in RN
TL;DR: In this paper, the existence and multiplicity of solutions for elliptic equations in R N, driven by a non-local integro-differential operator, which main prototype is the fractional Laplacian, was studied.
References
More filters
Journal ArticleDOI
Dual variational methods in critical point theory and applications
TL;DR: In this paper, general existence theorems for critical points of a continuously differentiable functional I on a real Banach space are given for the case in which I is even.
Journal ArticleDOI
An Extension Problem Related to the Fractional Laplacian
TL;DR: In this article, the square root of the Laplacian (−△) 1/2 operator was obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition.
Book
Critical Point Theory and Hamiltonian Systems
Jean Mawhin,Michel Willem +1 more
TL;DR: The direct method of the Calculus of Variations, Fenchel Transform and duality, Minimax Theorems for Indefinite Functional, Borsuk-Ulam Theorem and Index Theories, Lusternik-Schnirelman Theory and Multiple Periodic Solution with Fixed Energy, Morse-Ekeland Index, Morse Theory, and Morse Theory for Second Order Systems as discussed by the authors.
Journal ArticleDOI
Fractional Schrödinger equation.
TL;DR: The Hermiticity of the fractional Hamilton operator and the parity conservation law for fractional quantum mechanics are established and the energy spectra of a hydrogenlike atom and of a fractional oscillator in the semiclassical approximation are found.