Forced oscillation of second order linear and half-linear difference equations
نویسندگان
چکیده
منابع مشابه
Forced Oscillation of Second Order Linear and Half-linear Difference Equations
Oscillation properties of solutions of the forced second order linear difference equation ∆(rk∆xk) + ckxk+1 = hk are investigated. The authors show that if the forcing term h does not oscillate, in some sense, too rapidly, then the oscillation of the unforced equation implies oscillation of the forced equation. Some results illustrating this statement and extensions to the more general half-lin...
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This paper is concerned with a class of second order half-linear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing results. 2000 Mathematics Subject Classification: 34A30, 34C10.
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and Applied Analysis 3 exists, when σ t t here by s → t it is understood that s approaches t in the time scale and when x is continuous at t and σ t > t, xΔ t : x σ t − x t μ t . 1.7 Note that if T R, then the delta derivative is just the standard derivative, and when T Z the delta derivative is just the forward difference operator. Hence, our results contain the discrete and continuous cases a...
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A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of (1) is oscillatory, it is no restricti...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06811-9