Oscillation criteria for third-order linear differential equations
نویسندگان
چکیده
منابع مشابه
Oscillation Criteria for Third-order Functional Differential Equations with Damping
This paper is a continuation of the recent study by Bohner et al [9] on oscillation properties of nonlinear third order functional differential equation under the assumption that the second order differential equation is nonoscillatory. We consider both the delayed and advanced case of the studied equation. The presented results correct and extend earlier ones. Several illustrative examples are...
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By a solution of (.) wemean a function y(t) ∈ C[ty,∞) which has the property r(t)y′(t) ∈ C[ty,∞) and r(t)(r(t)y′(t))′ ∈ C[ty,∞) and satisfies (.) on [ty,∞) for every t ≥ ty ≥ t. We restrict our attention to those solutions of (.) which exist on I and satisfy the condition sup{|x(t)| : t ≥ t} > for any t ≥ ty. We assume that (.) possesses such a solution. A solution y(t) of (...
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where p(x) is a continuous positive function for 0<x< oo. Equation (1) is said to be nonoscillatory in (a, oo) if no solution of (1) vanishes more than once in this interval. Because of the Sturm separation theorem, this is equivalent to the existence of a solution which does not vanish at all in (a, oo). The equation will be called nonoscillatory—without the interval being mentioned —if there ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1961
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1961.11.919