Bounds on the Number of Poles of the Solution of a General Riccati Equation
A. Ronveaux, M. Cl. Dumont-Lepage, J. Habay · SIAM Journal on Mathematical Analysis · 1977
An elementary technique is used to give upper and lower bounds to the number of poles of the solutions of a general Riccati equation and asymptotic properties are also derived. Different applications of these bounds in the theory of second order linear differential equations give new results on the number of zeros or extrema of the solutions, on the characterization of eigenvalues and on the stability intervals in the periodic cases.