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Nonlinear Fractional Schrödinger Equations in R^N

  • Book
  • © 2021

Overview

Authors:
  1. Vincenzo Ambrosio

    1. Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Ancona, Italy

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  • Provides a set of results concerning nonlinear Schrödinger equations in the whole space driven by fractional operators
  • Deals with fractional Schrödinger equations involving different type of potentials and nonlinearities satisfying certain growth assumptions
  • Addressed to researchers interested in pure and applied mathematics, physics, mechanics, and engineering

Part of the book series: Frontiers in Mathematics (FM)

Part of the book sub series: Frontiers in Elliptic and Parabolic Problems (FEPP)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Preliminaries

    • Vincenzo Ambrosio
    Pages 1-34

  3. Some Abstract Results

    • Vincenzo Ambrosio
    Pages 35-49

  4. Fractional Scalar Field Equations

    • Vincenzo Ambrosio
    Pages 51-105

  5. Ground States for a Pseudo-Relativistic Schrödinger Equation

    • Vincenzo Ambrosio
    Pages 107-144

  6. Ground States for a Superlinear Fractional Schrödinger Equation with Potentials

    • Vincenzo Ambrosio
    Pages 145-194

  7. Fractional Schrödinger Equations with Rabinowitz Condition

    • Vincenzo Ambrosio
    Pages 195-254

  8. Fractional Schrödinger Equations with del Pino-Felmer Assumptions

    • Vincenzo Ambrosio
    Pages 255-294

  9. Fractional Schrödinger Equations with Superlinear or Asymptotically Linear Nonlinearities

    • Vincenzo Ambrosio
    Pages 295-334

  10. Multiplicity and Concentration Results for a Fractional Choquard Equation

    • Vincenzo Ambrosio
    Pages 335-362

  11. A Multiplicity Result for a Fractional Kirchhoff Equation with a General Nonlinearity

    • Vincenzo Ambrosio
    Pages 363-377

  12. Multiplicity and Concentration of Positive Solutions for a Fractional Kirchhoff Equation

    • Vincenzo Ambrosio
    Pages 379-415

  13. Concentrating Solutions for a Fractional Kirchhoff Equation with Critical Growth

    • Vincenzo Ambrosio
    Pages 417-441

  14. Multiplicity and Concentration Results for a Fractional Schrödinger-Poisson System with Critical Growth

    • Vincenzo Ambrosio
    Pages 443-481

  15. An Existence Result for a Fractional Kirchhoff–Schrödinger–Poisson System

    • Vincenzo Ambrosio
    Pages 483-496

  16. Multiple Positive Solutions for a Non-homogeneous Fractional Schrödinger Equation

    • Vincenzo Ambrosio
    Pages 497-519

  17. Sign-Changing Solutions for a Fractional Schrödinger Equation with Vanishing Potential

    • Vincenzo Ambrosio
    Pages 521-551

  18. Fractional Schrödinger Equations with Magnetic Fields

    • Vincenzo Ambrosio
    Pages 553-643

  19. Back Matter

    Pages 645-662
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Keywords

About this book

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.

Reviews

“The text offers a thourough overview of fractional Schrödinger equations in RN that can be used for a course at a graduate or Ph.D. level. A rich bibliography of more than three hundred references completes the book.” (Simone Secchi, zbMATH 1472.35003, 2021)

Authors and Affiliations

  • Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Ancona, Italy

    Vincenzo Ambrosio

Bibliographic Information

  • Book Title: Nonlinear Fractional Schrödinger Equations in R^N

  • Authors: Vincenzo Ambrosio

  • Series Title: Frontiers in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-60220-8

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-60219-2Published: 20 April 2021

  • eBook ISBN: 978-3-030-60220-8Published: 19 April 2021

  • Series ISSN: 1660-8046

  • Series E-ISSN: 1660-8054

  • Edition Number: 1

  • Number of Pages: XVII, 662

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Analysis, Operator Theory, Global Analysis and Analysis on Manifolds

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