Generalized Weierstrass Integrability of the Abel Differential Equations

Abstract

Abstract. We study the Abel differential equations that admits either a generalized Weierstrass first integral or a generalized Weierstrass inverse integrating factor.

Weierstrass integrability for a class of differential systems

“…In [9] and [10] the Weierstrass integrability has been characterized for the particular differential systems (1.1) with n = 3, 4.…”

Formal Weierstrass Nonintegrability Criterion for Some Classes of Polynomial Differential Systems in ℂ2

“…Note that there are systems which are Weierstrass integrable and are not Liouvillian integrable, see for instance system (6) and example 2 below. In the papers [19,20,21,23] are studied some Liénard differential systems and Abel differential equations that are Weierstrass integrable.…”

Generalized Weierstrass Integrability of a Class of Second-order Nonlinear Differential Equations

“…In this paper, we focus on generalized Weierstrass integrability. The definitions of generalized Weierstrass integrability and Weierstrass integrability were introduced in [4,5,6,7,8,9] and other papers. Now we restate them here.…”

“…We say that a differential system is generalized Weierstrass integrable [4,5,6,7,8,9] if it admits a first integral or an inverse integrating factor which is a generalized Weierstrass polynomial. We say that the differential system is Weierstrass integrable [4,5,6,7,8,9] if it admits a first integral or an inverse integrating factor which is a Weierstrass polynomial. The generalized Weierstrass integrability of the Liénard differential system has been studied, see [5].…”

“…The generalized Weierstrass integrability of the Liénard differential system has been studied, see [5]. In [6], the Weierstrass and the generalized Weierstrass integrability of the Abel differential equation have been considered. Related research can also be found in other papers [7,8,9,10,11] and the references therein.…”