Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

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Walter de Gruyter, 1996 - Mathematics - 547 pages

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Editor-in-Chief
Jürgen Appell, Würzburg, Germany

Honorary and Advisory Editors
Catherine Bandle, Basel, Switzerland
Alain Bensoussan, Richardson, Texas, USA
Avner Friedman, Columbus, Ohio, USA
Umberto Mosco, Worcester, Massachusetts, USA
Louis Nirenberg, New York, USA
Alfonso Vignoli, Rome, Italy

Editorial Board
Manuel del Pino, Bath, UK, and Santiago, Chile
Mikio Kato, Nagano, Japan
Wojciech Kryszewski, Toruń, Poland
Vicenţiu D. Rădulescu, Kraków, Poland
Simeon Reich, Haifa, Israel

Please submit book proposals to Jürgen Appell.

Titles in planning include

Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019)
Tomasz W. Dłotko and Yejuan Wang, Critical Parabolic-Type Problems (2019)
Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019)
Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020)
Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)
Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

 

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Contents

4
4
Introduction 1
4
3 Some equivalent characterizations of F and BS
49
Regular elliptic boundary value problems
99
Pointwise multiplication
142
Nemytskij operators in spaces of BesovTriebelLizorkin type
260
F and
290
P 9
377
Applications to semilinear elliptic boundary problems
393
Bibliography
525
Index
545
Copyright

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Page 526 - Church, PT, Timourian, JG, Folds and cusps in Banach spaces with applications to nonlinear partial differential equations I, Indiana Univ. Math. J. 34 (1985), 1-19; II, Trans.
Page 528 - On the existence of a nontrivial solution to nonlinear problems at resonance.
Page 525 - Abraham, R. and Robbin, J., Transversal Mappings and Flows, Benjamin, New York, 1967.
Page 530 - Runst, T., On the existence of solutions of a semilinear elliptic boundary value problem with superlinear nonlinearities.
Page 530 - P., On the resonance problem with nonlinearity which has arbitrary linear growth. J. Math. Anal.
Page 525 - Amann, H., Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In: Proc.
Page 526 - Dual variational methods in critical point theory and applications. J. funct. Analysis, 14 (1973), 349-381.
Page 531 - Boundary value problems with bounded nonlinearity and general null space of the linear part. Math. Z. 155 (1977), 129-138.

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