Mamonov, S. S. Determination of the number of limit cycles of the second kind for systems of differential equations. (Russian) Zbl 0656.34016 Differ. Uravn. 24, No. 6, 1076-1079 (1988). The number of limit cycles of the second kind is considered for the system \[ {\dot \sigma}=c^*x,\quad \dot x=Ax+\alpha_ s\frac{c^*x}{s^ 2+(c^*x)^ 2}b+\phi (\sigma)b, \] where \(x,b,c\in R^ n\); \(\alpha\),s are positive numbers, \(\phi\) (\(\sigma)\) is a periodic function satisfying the Lipschitz’s condition and is an \(n\times n\) matrix. Sufficient conditions for the existence of at least m limit cycles of the second kind are established. The case \(\alpha =0\) is also considered. Reviewer: I.Foltyńska MSC: 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations Keywords:first order differential equation; limit cycles of the second kind PDFBibTeX XMLCite \textit{S. S. Mamonov}, Differ. Uravn. 24, No. 6, 1076--1079 (1988; Zbl 0656.34016)