Oscillation and nonoscillation of forced second order dynamic equations
نویسندگان
چکیده
منابع مشابه
Oscillation and Nonoscillation of Forced Second Order Dynamic Equations
Oscillation and nonoscillation properties of second order Sturm–Liouville dynamic equations on time scales attracted much interest. These equations include, as special cases, second order self-adjoint differential equations as well as second order Sturm–Liouville difference equations. In this paper we consider a given (homogeneous) equation and a corresponding equation with forcing term. We giv...
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New oscillation and nonoscillation criteria are established for second order linear equations with damping and forcing terms. Examples are given to illustrate the results.
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In this paper, by introducing a nonnegative kernel function H(t, s), some oscillation criteria for a forced second-order dynamic equation on time scales are given. AMS Subject Classifications: 34K11, 34C10, 93C70.
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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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and Applied Analysis 3 In 10 , Leighton proved the following well-known oscillation test for 1.4 ; see 10, 11 . Theorem A see 10 . Assume that ∫∞ t0 1 A0 ( η )dη ∞, ∫∞ t0 A1 ( η ) dη ∞, 1.5 then 1.3 is oscillatory. This result for 1.4 was obtained by Wintner in 12 without imposing any sign condition on the coefficient A1. In 13 , Kneser proved the following result. Theorem B see 13 . Equation 1...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2007
ISSN: 0030-8730
DOI: 10.2140/pjm.2007.230.59