Periodic solutions for nonlinear nth order differential equations with delays

AbstractBy applying the continuation theorem of coincidence degree theory, we establish the existence of 2π-periodic solutions for a class of nonlinear nth order differential equations with delays

A liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment

We report on a hybrid optoelectronic integrated circuit based on a resonant tunnelling diode driving an optical communications laser diode. This circuit can act as a voltage controlled oscillator with optical and electrical outputs. We show that the oscillator operation can be described by Liénard's equation, a second order nonlinear differential equation, which is a generalization of the Van der Pol equation. This treatment gives considerable insight into the potential of a monolithic version of the circuit for optical communication functions including clock recovery and chaotic source applications

Periodic solutions to parameter-dependent equations with a \u3d5-Laplacian type operator

We study the periodic boundary value problem associated with the \u3d5-Laplacian equation of the form (\u3d5(u'))'+f(u)u'+g(t,u)=s, where s is a real parameter, f and g are continuous functions, and g is T-periodic in the variable t. The interest is in Ambrosetti\u2013Prodi type alternatives which provide the existence of zero, one or two solutions depending on the choice of the parameter s. We investigate this problem for a broad family of nonlinearities, under non-uniform type conditions on g(t,u) as u\u2192\ub1 1e. We generalize, in a unified framework, various classical and recent results on parameter-dependent nonlinear equations