Look Inside Variational Methods for Nonlocal Fractional Problems

Variational Methods for Nonlocal Fractional Problems

Part of Encyclopedia of Mathematics and its Applications

Authors:
Giovanni Molica Bisci, Università di Reggio Calabria, Italy
Vicentiu D. Radulescu, Institute of Mathematics of the Romanian Academy
Raffaella Servadei, Università degli Studi di Urbino, Italy

Jean Mawhin

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Date Published: March 2016
availability: Available
format: Hardback
isbn: 9781107111943

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Description

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
- Presents a modern, unified approach to analyzing nonlocal equations
- Examines a broad range of problems described by nonlocal operators that can be extended to other classes of related problems
- Reveals a number of surprising interactions among various topics
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Product details
- Date Published: March 2016
- format: Hardback
- isbn: 9781107111943
- length: 400 pages
- dimensions: 240 x 163 x 31 mm
- weight: 0.79kg
- availability: Available
Table of Contents
Foreword Jean Mawhin
Preface
Part I. Fractional Sobolev Spaces:
1. Fractional framework
2. A density result for fractional Sobolev spaces
3. An eigenvalue problem
4. Weak and viscosity solutions
5. Spectral fractional Laplacian problems
Part II. Nonlocal Subcritical Problems:
6. Mountain Pass and linking results
7. Existence and localization of solutions
8. Resonant fractional equations
9. A pseudo-index approach to nonlocal problems
10. Multiple solutions for parametric equations
11. Infinitely many solutions
12. Fractional Kirchhoff-type problems
13. On fractional Schrödinger equations
Part III. Nonlocal Critical Problems:
14. The Brezis–Nirenberg result for the fractional Laplacian
15. Generalizations of the Brezis–Nirenberg result
16. The Brezis–Nirenberg result in low dimension
17. The critical equation in the resonant case
18. The Brezis–Nirenberg result for a general nonlocal equation
19. Existence of multiple solutions
20. Nonlocal critical equations with concave-convex nonlinearities
References
Index.
Look Inside
Authors
Giovanni Molica Bisci, Università di Reggio Calabria, Italy
Giovanni Molica Bisci is Assistant Professor of Mathematical Analysis at the Università 'Mediterranea' di Reggio Calabria. He is the author of more than 90 research papers in nonlinear analysis.
Vicentiu D. Radulescu, Institute of Mathematics of the Romanian Academy
Vicentiu D. Radulescu is Distinguished Adjunct Professor at King Abdulaziz University in Jeddah, Saudi Arabia, and a professorial fellow at the 'Simion Stoilow' Mathematics Institute of the Romanian Academy. He is the author of several books and more than 200 research papers in nonlinear analysis. Since 2014 he is a Highly Cited Researcher (Thomson Reuters).
Raffaella Servadei, Università degli Studi di Urbino, Italy
Raffaella Servadei is Associate Professor of Mathematical Analysis at the Università degli Studi di Urbino 'Carlo Bo'. She has authored more than 40 research papers in nonlinear analysis.
Contributors
Jean Mawhin