Nonlinear Fractional Schrödinger Equations in R^N / by Vincenzo Ambrosio.

Format:

Book

Author/Creator:

Ambrosio, Vincenzo, author.

Series:

Frontiers in Elliptic and Parabolic Problems, 2730-5503

Language:

English

Subjects (All):

Differential equations.

Operator theory.

Global analysis (Mathematics).

Manifolds (Mathematics).

Differential Equations.

Operator Theory.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Differential Equations.

Operator Theory.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (669 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2021.

Summary:

<i>n< i=""></i>n This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.

Contents:

Preliminaries

Some abstract results

Fractional scalar field equations

Ground states for a pseudo-relativistic Schrödinger equation

Ground states for a superlinear fractional Schrödinger equation with potentials

Fractional Schrödinger equations with Rabinowitz condition

Fractional Schrödinger equations with del Pino-Felmer assumptions

Fractional Schrödinger equations with superlinear or asymptotically linear nonlinearities

Multiplicity and concentration results for a fractional Choquard equation

A multiplicity result for a fractional Kirchho equation with a general nonlinearity

Multiplicity and concentration of positive solutions for a fractional Kirchho equation

Concentrating solutions for a fractional Kirchho equation with critical growth

Multiplicity and concentration results for a fractional Schrödinger Poisson system with critical growth

An existence result for a fractional Kirchho -Schrödinger-Poisson system

Multiple positive solutions for a non-homogeneous fractional Schrödinger equation

Sign-changing solutions for a fractional Schrödinger equation with vanishing potentials

Fractional Schrödinger equations with magnetic fields.

Notes:

Includes bibliographical references and index.

ISBN:

3-030-60220-6

OCLC:

1249475057