Floquet Theory for Partial Differential Equations (Operator Theory: Advances and Applications) pdf epub fb2

Floquet Theory for Partial Differential Equations (Operator Theory: Advances and Applications) by - pdf epub fb2

Floquet Theory for Partial Differential Equations (Operator Theory: Advances and Applications) Author: -
Title: Floquet Theory for Partial Differential Equations (Operator Theory: Advances and Applications)
ISBN: 3764329017
ISBN13: 978-3764329013
Other Formats: azw mobi rtf txt
Pages: 354 pages
Publisher: Birkhäuser; 1993 edition (July 1, 1993)
Language: English
Category: Science & Math
Size PDF version: 1860 kb
Size EPUB version: 1533 kb
Subcategory: Mathematics




Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111­ 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103­ 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].