The spectral theory of periodic differential equations
Scottish Academic Press [distributed by Chatto & Windus, London, 1973 - 130 páginas
Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. 1975 edition.
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STABILITY AND INSTABILITY
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absolutely continuous alternative proof Bloch functions bounded Chapter Coddington and Levinson compact support complex-valued conditional stability intervals considered to hold constant continuous function continuously differentiable functions Corollary defined denote the eigenvalues differential equation differential operator double eigenvalue Eastham eigenfunction corresponding eigenfunctions eigenvalue problems exists fi2m finite number Floquet theory following theorem Fourier coefficients Fourier series gaps Gl(x Hence Hilbert space Hochstadt instability interval integral intervals of 2.1.1 ip(x Lemma Let p(x Levinson 17 linearly independent Magnus and Winkler matrix method multiplicity non-trivial solution non-zero number of zeros obtain Parseval formula periodic and semi-periodic periodic boundary conditions periodic problem piecewise continuous Pk(x positive integer proof of Theorem proves the theorem real number real-valued replaced satisfy self-adjoint self-adjoint operators semi-periodic problems solution with period solutions of 2.1.1 spectral theory spectrum t-periodic Titchmarsh 95 values vector Winkler 67 yn(x