The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in ℝ3 . An application concerning computation of a derivative of a scalar Poincaré mapping is given.
The paper describes asymptotic properties of a strongly nonlinear system $\dot{x}=f(t,x)$, $(t,x)\in \mathbb{R}\times \mathbb{R}^n$. The existence of an $\lfloor {}n/2\rfloor$ parametric family of solutions tending to zero is proved. Conditions posed on the system try to be independent of its linear approximation.