Oscillation and nonoscillation in linear delay or advanced difference equations
نویسندگان
چکیده
منابع مشابه
Oscillation and Nonoscillation of Even - Order Nonlinear Delay - Differential Equations
for their oscillatory and nonoscillatory nature. In Eqs. (1) and (2) y("(x) = (d%/dx')y{x), i = 1, 2, • • • , 2n; yr(x) = y(x — t(x))] dy/dx and d2y/dx2 will also be denoted by y' and y" respectively. Throughout this paper it will be assumed that p(x), j(x), t{x) are continuous real-valued functions on the real line (—°°, °°); j(x), p(x) and t(x), in addition, are nonnegative, r(x) is bounded a...
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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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We obtain some oscillation criteria for solutions of the nonlinear delay difference equation of the form xn+1−xn+pn ∏m j=1x αj n−kj = 0. 2000 Mathematics Subject Classification. 39A10.
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where {pi(n)} are sequences of nonnegative real numbers and not identically equal to zero, and ki is positive integer, i = 1,2, . . . , and is the first-order forward difference operator, xn = xn+1− xn, and xn = l−1( xn) for l ≥ 2. By a solution of (1.1) or inequality (1.2), we mean a nontrival real sequence {xn} satisfying (1.1) or inequality (1.2) for n ≥ 0. A solution {xn} is said to be osci...
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The oscillatory behavior of some differential and difference equations have been investigated (see, for instance, [1], [3], [4], [5]). In recent years, the oscillations of discrete analogues of delay differential equations have been given [2], [7]. Furthermore, explicit conditions for the oscillation of difference equations with constant coefficients have been studied [6]. Erbe and Zhang [2] ha...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 1998
ISSN: 0895-7177
DOI: 10.1016/s0895-7177(98)00033-8