Non-oscillation Domains of Differential Equations with Two ParametersThis research monograph is an introduction to single linear differential equations (systems) with two parameters and extensions to difference equations and Stieltjes integral equations. The scope is a study of the values of the parameters for which the equation has one solution(s) having one (finitely many) zeros. The prototype is Hill's equation or Mathieu's equation. For the most part no periodicity assumptions are used and when such are made, more general notions such as almost periodic functions are introduced, extending many classical and introducing many new results. Many of the proofs in the first part are variational thus allowing for natural extensions to more general settings later. The book should be accessible to graduate students and researchers alike and the proofs are, for the most part, self-contained. |
Contents
Scalar VolterraStieltjes integral equations | 4 |
Linear Vector Ordinary Differential Equations | 49 |
Bibliography | 101 |
Copyright | |
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Other editions - View all
Non-Oscillation Domains of Differential Equations with Two Parameters Angelo B. Mingarelli,S. Gotskalk Halvorsen No preview available - 1988 |
Common terms and phrases
almost-periodic functions assume assumption Besicovitch Bohr almost-periodic bounded bounded set changes sign class of potentials closed set constant contains continuous convex Corollary defined Differential Equations DIPRO disconjugacy domain disconjugate Edited equal to zero Euler equation example exists fixed full ray Hence implies inf v(x integral interval of non-oscillation Lebesgue measure lemma Let A(x Let f ESL Let q lim inf lim sup linearly dependent Lloc Loc(I matrix mean value equal Moreover necessary condition non-oscillation domain non-oscillatory oscillating potential oscillatory at infinity parabola parameter space periodic functions permutation matrix polynomial positive Lebesgue measure positive linear functional Proceedings proof of theorem q ESL Remark resp satisfy sequence set of positive solution y(x space Rē Sturm comparison theorem sufficiently large sup v(x symmetric trigonometric polynomials unbounded vector Wintner-disconjugate yn(x Zn(x ΧΕΙ