**Laszlo Hatvani**

## On The Armellini-Tonelli-Sansone Theorem The Navier-Stokes System

**abstract:**

Sufficient conditions are given guaranteeing that all solutions of the
equation
$$
x''+a(t)f(x)=0\;\;\;(xf(x)>0)
$$
tend to zero as $t$ goes to infinity. The conditions contain integrals instead
of maxima and minima in earlier results. Finally, a probabilistic
generalization of Armellini-Tonelli-Sansone theorem is formulated.

**Mathematics Subject Classification:**
34D20.

**Key words and phrases:**
Partial asymptotic stability, oscillation.