Bifurcation properties for a sequence of approximation of delay equations (Q1206971)

The purpose of the paper is to investigate properties of the differential equations \(\dot x=\lambda f(x(t),\) \(x(t-1))\) and its approximation by difference equations. In section II the authors show that in any segment \([\varphi,\psi]\) of initial values (where \(\varphi<0<\psi)\) there is at least one initial value of an oscillating solution which is the limit of a sequence of initial values for the approximating equations. The results in section III contain information about bifurcation of Rabinowitz type.