On successive approximation for solving the Cauchy problem for a system of linear generalized ordinary differential equations.
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).
The paper investigates the singular initial problem[4pt] [4pt] on the half-line . Here , where , and are zeros of , which is locally Lipschitz continuous on . Function is continuous on , has a positive continuous derivative on and . Function is continuous on and positive on . For specific values we prove the existence and uniqueness of damped solutions of this problem. With additional conditions for , and it is shown that the problem has for each specified a unique...
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.