Bifurcation of singular points of differential-functional equations
Bifurcation of singular points of the system \[ (1)\quad dx/dt=L(\epsilon)x_ t+f(t,x_ t,\epsilon) \] is considered, where \(\epsilon\) is a small parameter, L(\(\epsilon)\): \(C\to R^ n\) is a linear continuous functional, \(f(t+T,\phi,\epsilon)=f(t,\phi,\epsilon),\) \(T>0\); \(f(t,\phi,\epsilon)=O(| \phi |^ 2)\) as \(| \phi | \to 0\) and f(t,\(\phi\),\(\epsilon)\) is a functional continuous with respect to t and \(\epsilon\) and four times differentiabe with respect to \(\phi\). A method for finding a solution to (1) is presented.
scientific article; zbMATH DE number 3989814