Periodic solutions of autonomous systems of difference and difference-differential equations with a small delay

In the present paper the method of the equivalent differential-operator equation has been applied in the study of the existence and asymptotic representation of periodic solutions of autonomous systems of the form     

Holomorphic complex differential equations: An elementary proof that the time-p map is holomorphic

We give an elementary proof that, in its domain of definition, the time-p map of a scalar, autonomous holomorphic, complex differential equation, is itself holomorphic. This result is used by Sverdlove [1] when considering limit cycles in complex holomorphic differential equations. However no proof or reference for the result is given in [1]. Although this result must be well established, a proof does not appear to be readily accessible in the reference literature.     

Asymptotic forms of positive solutions of quasilinear ordinary differential equations with singular nonlinearities

In this paper we consider positive solutions of second order quasilinear ordinary differential equations with singular nonlinearities. We obtain asymptotic equivalence theorems for asymptotically superlinear solutions and decaying solutions. By using these theorems, exact asymptotic forms of such solutions are determined. Furthermore, we can establish the uniqueness of decaying solutions as an application of our results.     

Asymptotic behavior of the unbounded solutions of some boundary layer equations

We give an asymptotic equivalent at infinity of the unbounded solutions of some boundary layer equations arising in fluid mechanics.Received: 24 May 2004     

Homoclinic and heteroclinic orbits for a class of Hamiltonian systems

The existence of a rich structure of homoclinic and heteroclinic solutions is established for a family of Hamiltonian systems that serve as a simpler model for the multiple pendulum system. The proof is based on recently developed arguments from the calculus of variations that have proved useful in finding actual solutions of an equation near approximate solution.This research was sponsorted in part by the National Science Foundation under grant #MCS-8110556 and the U. S. Army Research Office under Contract #DAAL03-87-K-0043. Any reproduction for the purpose of the United States Government is permitted.     

Quasilinearization for functional differential equations with retardation and anticipation

The technique of generalised quasilinearization is developed, using the method of lower and upper solutions and the monotone iterative technique (MIT), to prove the existence of unique solutions for functional differential equations (FDE) with retardation and anticipation.     

Monotone iterative technique for functional differential equations with retardation and anticipation

The method of the monotone iterative technique together with coupled lower and upper solutions is employed to prove existence and uniqueness results for functional differential equations involving retardation and anticipation.