
Partial Differential Equations with Variable Exponents
Variational Methods and Qualitative Analysis
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 24. June 2015
Book
Hardback
324 pages
978-1-4987-0341-3 (ISBN)
Description
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.
The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences.
The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis.
The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.
The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences.
The analysis developed in the book is based on the notion of a generalized or weak solution. This approach leads not only to the fundamental results of existence and multiplicity of weak solutions but also to several qualitative properties, including spectral analysis, bifurcation, and asymptotic analysis.
The book examines the equations from different points of view while using the calculus of variations as the unifying theme. Readers will see how all of these diverse topics are connected to other important parts of mathematics, including topology, differential geometry, mathematical physics, and potential theory.
More details
Series
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Product notice
sewn/stitched
Cloth over boards
Illustrations
11 s/w Abbildungen, 2 s/w Tabellen
2 Tables, black and white; 11 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 157 mm
Thickness: 23 mm
Weight
635 gr
ISBN-13
978-1-4987-0341-3 (9781498703413)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Vicentiu D. Radulescu | Dusan D. Repovs
Partial Differential Equations with Variable Exponents
Variational Methods and Qualitative Analysis
E-Book
06/2015
Chapman and Hall
€225.99
Available for download

Vicentiu D. Radulescu | Dusan D. Repovs
Partial Differential Equations with Variable Exponents
Variational Methods and Qualitative Analysis
E-Book
06/2015
Chapman & Hall/CRC
€225.99
Available for download
Persons
Vicentiu D. Radulescu is a distinguished adjunct professor at the King Abdulaziz University of Jeddah, a professorial fellow at the "Simion Stoilow" Mathematics Institute of the Romanian Academy, and a professor of mathematics at the University of Craiova. He is the author of several books and more than 200 research papers in nonlinear analysis. He is a Highly Cited Researcher (Thomson Reuters) and a member of the Accademia Peloritana dei Pericolanti. He received his Ph.D. from the Universite Pierre et Marie Curie (Paris 6).
Dusan D. Repovs is a professor of geometry and topology at the University of Ljubljana and head of the Topology, Geometry and Nonlinear Analysis Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana. He is the author of several books and more than 300 research papers in topology and nonlinear analysis. He is a member of the New York Academy of Sciences, the European Academy of Sciences, and the Engineering Academy of Slovenia. He received his Ph.D. from Florida State University.
Dusan D. Repovs is a professor of geometry and topology at the University of Ljubljana and head of the Topology, Geometry and Nonlinear Analysis Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana. He is the author of several books and more than 300 research papers in topology and nonlinear analysis. He is a member of the New York Academy of Sciences, the European Academy of Sciences, and the Engineering Academy of Slovenia. He received his Ph.D. from Florida State University.
Content
Isotropic and Anisotropic Function Spaces: Lebesgue and Sobolev Spaces with Variable Exponent. Variational Analysis of Problems with Variable Exponents: Nonlinear Degenerate Problems in Non-Newtonian Fluids. Spectral Theory for Differential Operators with Variable Exponent. Nonlinear Problems in Orlicz-Sobolev Spaces. Anisotropic Problems: Continuous and Discrete: Anisotropic Problems. Difference Equations with Variable Exponent. Appendices. Bibliography. Index.