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On the asymptotic behavior for a damped oscillator under a sublinear friction.

Jesús Ildefonso Díaz, Amable Liñán (2001)

RACSAM

Mostramos la existencia de dos curvas de datos iniciales (x0, v0) para las cuales las soluciones x(t) correspondientes del problema de Cauchy asociado a la ecuación xtt + |xt|α-1 xt + x = 0, supuesto α ∈ (0,1), se anulan idénticamente después de un tiempo finito. Mediante métodos asintóticos y argumentos de comparación mostramos que para muchos otros datos iniciales las soluciones decaen a 0, en un tiempo infinito, como t-α / (1-α).

On the Existence of Oscillatory Solutions of the Second Order Nonlinear ODE

Martin Rohleder (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper investigates the singular initial problem[4pt] ( p ( t ) u ' ( t ) ) ' + q ( t ) f ( u ( t ) ) = 0 , u ( 0 ) = u 0 , u ' ( 0 ) = 0 [4pt] on the half-line [ 0 , ) . Here u 0 [ L 0 , L ] , where L 0 , 0 and L are zeros of f , which is locally Lipschitz continuous on . Function p is continuous on [ 0 , ) , has a positive continuous derivative on ( 0 , ) and p ( 0 ) = 0 . Function q is continuous on [ 0 , ) and positive on ( 0 , ) . For specific values u 0 we prove the existence and uniqueness of damped solutions of this problem. With additional conditions for f , p and q it is shown that the problem has for each specified u 0 a unique...

On the Factorization of the Poincaré Polynomial: A Survey

Akyıldız, Ersan (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.Factorization is an important and very difficult problem in mathematics. Finding prime factors of a given positive integer n, or finding the roots of the polynomials in the complex plane are some of the important problems not only in algorithmic mathematics but also in cryptography.

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