Planar nonautonomous polynomial equations: The Riccati equation

Abstract

We give a few sufficient conditions for the existence of two periodic solutions of the Riccati ordinary differential equation in the plane. We give also examples of the equation without periodic solutions.

Planar nonautonomous polynomial equations IV. Nonholomorphic case

“…It is possible to consider a 1 ∈ C(R, C) (cf. [22,Subsection 3.1], [23,Section 3]), provided the equality…”

“…The presented paper is a continuation of [21][22][23]. We study a planar nonautonomous differential equations of the forṁ z = v(t, z) = where n > r ≥ 1 and a j , c k ∈ C(R, C) are T -periodic.…”

“…We develop the idea from [21][22][23] and give a few sufficient conditions for the existence of one or two periodic solutions. We deal with the condition of geometric type which corresponds to the ones from [22,Subsection 3.1] and [23].…”

“…We deal with the condition of geometric type which corresponds to the ones from [22,Subsection 3.1] and [23]. Namely, we try to include sets a j (R) and c k (R) in some sectors of the complex plane.…”

Planar nonautonomous polynomial equations V. The Abel equation

“…The only exception is the Riccati equation (n = 2), where the Poincaré map is just a Möbius transformation [1]. The present paper is a continuation of [4][5][6][7] and is devoted to the full description of the dynamics of the Abel equation of the forṁ…”