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An improvement to Darboux integrability theorem for systems having a center |
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| Authors: | J Chavarriga |
| Institution: | Departament de Matemàtiques, Universitat de Lleida Avda. Jaume II 69, 25001, Lleida, Spain Laboratoire de Mathématique et Physique Théorique, Faculté des Sciences et Techniques Université de Tours, Parc de Grandmont, 37200, Tours, France Departament de Matemàtiques, Universitat de Lleida Avda. Jaume II 69, 25001, Lleida, Spain |
| Abstract: | We consider planar polynomial differential systems of degree m with a center at the origin and with an arbitrary linear part. We show that if the system has m(m + 1)/2 ? (m + 1)/2] algebraic solutions or exponential factors then it has a Darboux integrating factor. This result is an improvement of the classical Darboux integrability theorem and other recent results about integrability. |
| Keywords: | Nonlinear differential equations Integrability Center problem |
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