ISBN-13: 9783764329013 / Angielski / Twarda / 1993 / 354 str.
ISBN-13: 9783764329013 / Angielski / Twarda / 1993 / 354 str.
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].