  This article deals with the asymptotic behavior of fourth order differential
equation where the coefficients are perturbations of linear constant
coefficient equation. We introduce a change of variable and deduce that the new
variable satisfies a third order differential equation of Riccati type. We
assume three hypothesis. The first is the following: all roots of the
characteristic polynomial associated to the fourth order linear equation has
distinct real part. The other two hypothesis are related with the behavior of
the perturbation functions. Under this general hypothesis we obtain four main
results. The first two results are related with the application of fixed point
theorem to prove that the Riccati equation has a unique solution. The next
result concerns with the asymptotic behavior of the solutions of the Riccati
equation. The fourth main theorem is introduced to establish the existence of a
fundamental system of solutions and to precise formulas for the asymptotic
behavior of the linear fourth order differential equation.
