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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, 157160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [8789, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406408], 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 socalled Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called FloquetLyapunov theorem) [120, 267].
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As a grad student specializing in differential equations, this book is a fantastic addition to my library. The depth of coverage on operator theory is impressive, and the applications section is super helpful. Definitely worth the investment!
M
Maya Zhang
Great resource for PDEs!
I picked up 'The Floquet Theory for Partial Differential Equations' for my advanced math course, and it's been indispensable. The explanations are thorough, making complex concepts much clearer. Highly recommend it for anyone in operator theory courses!
C
Carlos Mendes
Useful but dense at times
This book has a lot of valuable information on Floquet theory, but I found some sections really hard to digest. If you're looking for a deep dive into operator theory, this is a solid choice, just be prepared to spend time on it.
E
Emma Johnson
Not what I expected
I thought this book would be more straightforward, but it dives deep into technical details that can be overwhelming. The applications are interesting, but the layout could be clearer. It’s not bad, just not what I was hoping for.
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