Linear differential equations where nonoscillation is equivalent to eventual disconjugacy
نویسندگان
چکیده
منابع مشابه
Nonoscillation and disconjugacy of systems of linear differential equations
The differential equations under consideration are of the form (1) §f = A(t)x, where A(t) is a piecewise continuous real nxn-matrix on a real interval a, and the vector x = (x-j...,x ) is continuous on a. The equation is said to be nonoscillatory on a if every nontrivial real solution vector x has at least one component xv which does not vanish on a. The principal concern of this paper is the d...
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Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established. 1. Statement of the Problem and Formulation of Basic Results Consider the differential equation u′′ + p(t)u = 0, (1) where p : [0, +∞[→ [0, +∞[ is an integrable function. By a solution of equation (1) is understood a function u : [0,+∞[→] − ∞, +∞[ which is locally absolutely continuous tog...
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His basic criterion for disconjugacy turned out to be 1 0 is continuous and fal/P= °°, then the substitution t — fll/p transforms the first equation into one where p = l and the new f-interval is infinite. Thus this more general case reduces to Nehari's and again the criterion is 1 <X(o). However part of the whole picture seems to be lost by this transformation. If Ial...
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where a(t) is a locally integrable function of /. We call equation (1) oscillatory if all solutions of (1) have arbitrarily large zeros on [0, oo), otherwise, we say equation (1) is nonoscillatory. As a consequence of Sturm's Separation Theorem [21], if one of the solutions of (1) is oscillatory, then all of them are. The same is true for the nonoscillation of (1). The literature on second orde...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0364759-x