منابع مشابه
Oscillation of Fractional Nonlinear Difference Equations
The oscillation criteria for forced nonlinear fractional difference equation of the form ∆x(t) + f1(t, x(t+ α)) =v(t) + f2(t, x(t+ α)), t ∈ N0, 0 < α ≤ 1, ∆x(t)|t=0 =x0, where ∆α denotes the Riemann-Liouville like discrete fractional difference operator of order α is presented. Mathematics Subject Classification: 26A33, 39A12
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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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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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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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We obtain the complete classification of oscillation and nonoscillation for the q-difference equation x(t) + b(−1) tc x(qt) = 0, b 6= 0, where t = q ∈ T = qN0 , q > 1, c, b ∈ R. In particular we prove that this q-difference equation is nonoscillatory, if c > 2 and is oscillatory, if c < 2. In the critical case c = 2 we show that it is oscillatory, if |b| > 1 q(q−1) , and is nonoscillatory, if |...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1993
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-65-1-25-32