AbstractWe show that the system xdot = ydot = 2n+2xy+y2 has the algebraic solution h(x, y) = Hn(x)y + 2nHn−1(x), where Hn(x) is the Hermite polynomial of degree n, and the system is not Darboux integrable and has no Darboux integrating factor for any n ϵ N
Abstract. We consider the class of polynomial differential equations x ̇ = Pn(x, y)+Pn+1(x, y) +Pn+2...
We provide the necessary and sufficient conditions of Liouvillian integrability for Li\'{e}nard diff...
We study the integrability of two-dimensional autonomous systems in the plane of the form $\dotx=-y+...
AbstractWe show that the system xdot = ydot = 2n+2xy+y2 has the algebraic solution h(x, y) = Hn(x)y ...
Agraïments: The first and third authors are partially supported by NNSF of China grant No. 10671123 ...
Abstract: The paper is divided into two parts. In the first one we present a survey about the theory...
The paper is divided into two parts. In the first one we present a survey about the theory of Darbou...
Abstract In this article we summarize the results on algebraic aspects of integrability for polynomi...
Agraïments: The first and third author is partially supported by the Algerian Ministry of Higher Edu...
We deal with complex planar differential systems having a Darboux first integral H. We present a def...
AbstractWe consider the class of polynomial differential equations x˙=λx-y+Pn(x,y),y˙=x+λy+Qn(x,y), ...
AbstractWe deal with complex planar differential systems having a Darboux first integral H. We prese...
The Darbouxian theory of integrability allows to determine when a polynomial differential system in ...
AbstractFor a class of polynomial differential systems of degree (m1,…,md) in Rd which is open and d...
We present an introductory survey to the Darboux integrability theory of planar complex and real pol...
Abstract. We consider the class of polynomial differential equations x ̇ = Pn(x, y)+Pn+1(x, y) +Pn+2...
We provide the necessary and sufficient conditions of Liouvillian integrability for Li\'{e}nard diff...
We study the integrability of two-dimensional autonomous systems in the plane of the form $\dotx=-y+...
AbstractWe show that the system xdot = ydot = 2n+2xy+y2 has the algebraic solution h(x, y) = Hn(x)y ...
Agraïments: The first and third authors are partially supported by NNSF of China grant No. 10671123 ...
Abstract: The paper is divided into two parts. In the first one we present a survey about the theory...
The paper is divided into two parts. In the first one we present a survey about the theory of Darbou...
Abstract In this article we summarize the results on algebraic aspects of integrability for polynomi...
Agraïments: The first and third author is partially supported by the Algerian Ministry of Higher Edu...
We deal with complex planar differential systems having a Darboux first integral H. We present a def...
AbstractWe consider the class of polynomial differential equations x˙=λx-y+Pn(x,y),y˙=x+λy+Qn(x,y), ...
AbstractWe deal with complex planar differential systems having a Darboux first integral H. We prese...
The Darbouxian theory of integrability allows to determine when a polynomial differential system in ...
AbstractFor a class of polynomial differential systems of degree (m1,…,md) in Rd which is open and d...
We present an introductory survey to the Darboux integrability theory of planar complex and real pol...
Abstract. We consider the class of polynomial differential equations x ̇ = Pn(x, y)+Pn+1(x, y) +Pn+2...
We provide the necessary and sufficient conditions of Liouvillian integrability for Li\'{e}nard diff...
We study the integrability of two-dimensional autonomous systems in the plane of the form $\dotx=-y+...
DOI
Add to ORKG