On the existence of a bounded solution of a non-linear differential equation
In the paper we consider the growth of entire solution of a nonlinear differential equation and improve some existing results.
For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...
Scopo della presente Nota è quello di fornire una maggiorazione della lunghezza dell'intervallo sul quale il problema (1) (2) (3) ammette soltanto la soluzione nulla.
In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.