Asymptotic and oscillatory behavior of nth order forced functional differential equations
نویسندگان
چکیده
منابع مشابه
Oscillations of Nth-order Functional Differential Equations
-Some new oscillation criteria for the even order damped functional differential equation (a(t)z(n-1)(t)) ' ÷ p(t)lz(n-1)(Ol#x(n-a)(O ÷ q(t)f(xIaa(t)] . . . . . =Lq.~(t)]) = 0 are established, where ~ _> O. These criteria are an extension of some of the known results. 1. I N T R O D U C T I O N Recently, Grace and Lalli [1] discussed the oscillation of the nth-order functional differential equa...
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In this paper, we study the n th-order half-linear dynamic equations (x[n−1])Δ (t)+ p(t)φα[1,n−1] (x(g(t))) = 0 on an above-unbounded time scale T , where n 2 , x[i](t) := ri(t)φαi [( x[i−1] )Δ (t) ] , i = 1, . . . ,n−1, with x[0] = x, φβ (u) := |u|β sgnu , and α [i, j] := αi · · ·α j . Criteria are obtained for the asymptotics and oscillation of solutions for both even and odd order cases. Thi...
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where n >, 2, a: [0, 00) + [0, a~), q: [0, co) --+ (-00, co), andf: (--co, 03) + (-00, CQ). We assume a(l), q(t), andf( x are continuous, q(t) < t for all t > 0, q(t) 3 co ) as t ---f co, and xf(x) > 0 for x # 0. Usually, a condition of monotonicity on f is needed in order to obtain results for Eq. (1) analogous to those of an ordinary differential equation of the same type. Many authors observ...
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where ∆ is the forward difference operator defined by ∆xn = xn+1 −xn, α and β are positive constants, {pn} and {qn} are positive real sequences defined for all n ∈ N(n0) = {n0, n0 + 1, ...}, and n0 a nonnegative integer. By a solution of equation (1), we mean a real sequence {xn} that satisfies equation (1) for all n ∈ N(n0). If any four consecutive values of {xn} are given, then a solution {xn...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1989
ISSN: 0022-247X
DOI: 10.1016/0022-247x(89)90090-5