Results of the Landesman–Lazer type provide necessary and sufficient conditions for the existence of periodic solutions of certain nonlinear differential equations with forcing. Typically, they deal with scalar problems. This paper presents a discussion of possible extensions to systems. The emphasis is placed on the new phenomena produced by the increase… (More)
The main goal of this paper is to study analytically the families of symmetric periodic orbits of the elliptic Sitnikov problem for all values of the eccentricity in the interval [0, 1). The basic tool for proving our results is the global continuation method of the zeros of a function depending on one–parameter provided by Leray and Schauder and based in… (More)
A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are… (More)
Given the equations of motion of a system of particles, it is always possible to find a small time-dependent perturbation such that most solutions escape to infinity. The unperturbed system is autonomous and has no dissipation.
We consider a forced harmonic oscillator at resonance with a nonlinear perturbation and obtain a sharp condition for the existence of unbounded motions. Such a condition is extended to the case of a semilinear vibrating string.
An anesthesiologist must remain vigilant of the patient's clinical status, incorporating many independent physiological measurements. Oxygen saturation and heart rate are represented by continuous audible tones generated by the pulse oximeter, a mandated monitoring device. Other important clinical parameters--notably blood pressure--lack any audible… (More)