On structure of solutions of a system of four differential inequalities.
We investigate the nonautonomous periodic system of ODE’s of the form , where is a -periodic function defined by for , for and the vector fields and are related by an involutive diffeomorphism.
Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation with , real (not necessarily natural) , and continuous functions and defined in a neighborhood of . For this equation with positive potential a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. Sufficient conditions are obtained...
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).
We apply the averaging method to ordinary differential inclusions with maxima perturbed by a small parameter and illustrate the method by some examples.