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Partial Differential Equations with Variable Exponents Variational Methods and Qualitative Analysis

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Dettagli

Genere:Libro
Lingua: Inglese
Pubblicazione: 06/2015
Edizione: 1° edizione





Note Editore

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.




Sommario

Isotropic and Anisotropic Function Spaces Lebesgue and Sobolev Spaces with Variable Exponent History of function spaces with variable exponent Lebesgue spaces with variable exponent Sobolev spaces with variable exponent Dirichlet energies and Euler–Lagrange equations Lavrentiev phenomenon Anisotropic function spaces Orlicz spaces Variational Analysis of Problems with Variable ExponentsNonlinear Degenerate Problems in Non-Newtonian Fluids Physical motivation A boundary value problem with nonhomogeneous differential operator Nonlinear eigenvalue problems with two variable exponents A sublinear perturbation of the eigenvalue problem associated to the Laplace operator Variable exponents versus Morse theory and local linking The Caffarelli–Kohn–Nirenberg inequality with variable exponent Spectral Theory for Differential Operators with Variable ExponentContinuous spectrum for differential operators with two variable exponents A nonlinear eigenvalue problem with three variable exponents and lack of compactness Concentration phenomena: the case of several variable exponents and indefinite potentialAnisotropic problems with lack of compactness and nonlinear boundary condition Nonlinear Problems in Orlicz–Sobolev Spaces Existence and multiplicity of solutions A continuous spectrum for nonhomogeneous operators Nonlinear eigenvalue problems with indefinite potential Multiple solutions in Orlicz–Sobolev spacesNeumann problems in Orlicz–Sobolev spaces Anisotropic Problems: Continuous and Discrete Anisotropic Problems Eigenvalue problems for anisotropic elliptic equations Combined effects in anisotropic elliptic equations Anisotropic problems with no-flux boundary condition Bifurcation for a singular problem modelling the equilibrium of anisotropic continuous media Difference Equations with Variable Exponent Eigenvalue problems associated to anisotropic difference operatorsHomoclinic solutions of difference equations with variable exponentsLow-energy solutions for discrete anisotropic equations Appendix A: Ekeland Variational Principle Appendix B: Mountain Pass Theorem Bibliography Index A Glossary is included at the end of each chapter.




Autore

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 Université Pierre et Marie Curie (Paris 6). Dušan D. Repovš 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.










Altre Informazioni

ISBN:

9781498703413

Condizione: Nuovo
Collana: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Dimensioni: 9.25 x 6.25 in Ø 1.35 lb
Formato: Copertina rigida
Illustration Notes:11 b/w images and 2 tables
Pagine Arabe: 324


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