Variational methods for nonlocal fractional problems
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 beg…
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- Full title :Variational methods for nonlocal fractional problems / Giovanni Molica Bisci, Università 'Mediterranea' di Reggio Calabria, Italy, Vicentiu D. Radulescu, Institute of Mathematics of the Romanian Academy, Raffaella Servadei, Università degli Studi di Urbino 'Carlo Bo', Italy.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©2016
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:©2016
The Physical Object
- Description:1 online resource (xvi, 383 pages)
Edition Identifiers
- ISBN:9781316282397, 1316282392, 9781316574997, 1316574997
- oclc:ocn944382493
- LC Classification:QA314
- Dewey Decimal:515.83
Table of Contents
Part I Fractional Sobolev spaces -- Fractional framework -- A density result for fractional Sobolev spaces -- An eigenvalue problem -- Weak and viscosity solutions -- Spectral fractional Laplacian problems -- Part II Nonlocal subcritical problems -- Mountain pass and linking results -- Existence and localization of solutions -- Resonant fractional equations -- A pseudoindex approach to nonlocal problems -- Multiple solutions for parametric equations -- Infinitely many solutions -- Fractional Kirchhoff-type problems -- On fractional Schrodinger equations -- Part III Nonlocal critical problems -- The Brezis-Nirenberg result for the fractional Laplacian -- Generalization of the Brezis-Nirenberg result -- The Brezis-Nirenberg result in low dimension -- The critical equation in the resonant case -- The Brezis-Nirenberg result for a general nonlocal equation -- Existence of multiple solutions -- Non critical equations with concave-convex nonlineaarities.
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