52,527 research outputs found
Existence results on positive periodic solutions for impulsive functional differential equations
A class of first order nonlinear functional differential equations with impulses is studied. It is shown that there exist one or two positive T-periodic solutions under certain assumptions, and no positive T-periodic solution under some other assumptions. Applications to some impulsive biological models and an example, which can not be covered by known results, are given to illustrate the main results
Orbital stability of periodic waves in the class of reduced Ostrovsky equations
Periodic travelling waves are considered in the class of reduced Ostrovsky
equations that describe low-frequency internal waves in the presence of
rotation. The reduced Ostrovsky equations with either quadratic or cubic
nonlinearities can be transformed to integrable equations of the Klein--Gordon
type by means of a change of coordinates. By using the conserved momentum and
energy as well as an additional conserved quantity due to integrability, we
prove that small-amplitude periodic waves are orbitally stable with respect to
subharmonic perturbations, with period equal to an integer multiple of the
period of the wave. The proof is based on construction of a Lyapunov
functional, which is convex at the periodic wave and is conserved in the time
evolution. We also show numerically that convexity of the Lyapunov functional
holds for periodic waves of arbitrary amplitudes.Comment: 34 page
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
Nonzero solutions of perturbed Hammerstein integral equations with deviated arguments and applications
We provide a theory to establish the existence of nonzero solutions of
perturbed Hammerstein integral equations with deviated arguments, being our
main ingredient the theory of fixed point index. Our approach is fairly general
and covers a variety of cases. We apply our results to a periodic boundary
value problem with reflections and to a thermostat problem. In the case of
reflections we also discuss the optimality of some constants that occur in our
theory. Some examples are presented to illustrate the theory.Comment: 3 figures, 23 page
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