On the asymptotic expansion of the Airy function
Si prova una nuova formula di rappresentazione per la famosa funzione di Airy. Ne viene data applicazione per la determinazione di certi bounds significativi per la funzione stessa.
On the behaviour of solutions of the differential equations
On the existence of solutions of the singular Cauchy problem for systems of differential equations not solved with respect to the derivatives.
On the functional integrability and asymptotic behaviours of a certain differential equation with delay
On the Liouville-type transformation for differential systems
On the step-type contrast structure of a second-order semilinear differential equation with integral boundary conditions.
Oscillating rivers. (Fleuves oscillants.)
Oscillation and asymptotic properties of strongly sublinear differential equations with deviating arguments
Oscillation criteria for certain nonlinear fourth order equations.
Oscillations of superlinear differential equations with deviating arguments
Oscillatory and asymptotic properties of third and fourth order linear differential equations
Overstability and resonance
We consider a singularity perturbed nonlinear differential equation which we suppose real analytic for near some interval and small , . We furthermore suppose that 0 is a turning point, namely that is positive if . We prove that the existence of nicely behaved (as ) local (at ) or global, real analytic or solutions is equivalent to the existence of a formal series solution with analytic at . The main tool of a proof is a new “principle of analytic continuation” for such “overstable” solutions....