Bifurcation equation for planar systems of differential equations
The author establishes conditions for the existence of small periodic solutions of the equations \[ \dot x=\alpha (\epsilon)x- y+g(x,y,\epsilon),\quad \dot y=x+\alpha (\epsilon)y+h(x,y,\epsilon) \] and \(\ddot y-2\alpha(\epsilon)\dot y+y= f(\dot y,y,\epsilon),\) where \(g=O(x^ 2+y^ 2)\), \(h=O(x^ 2+y^ 2)\) and \(f=O(\dot y^ 2+y^ 2)\). He also discusses their stability.
scientific article; zbMATH DE number 4097840