RT info:eu-repo/semantics/article
T1 Existence and convergence of Puiseux series solutions for autonomous first order differential equations
A1 Cano Torres, José María
A1 Sendra Pons, Juan Rafael
A1 Falkensteiner, Sebastian
K1 Algebraic differential equation Algebraic curve Place Formal Puiseux series solution Convergent solution
AB Given an autonomous first order algebraic ordinary differential equation , we prove that every formal Puiseux series solution of , expanded around any finite point or at infinity, is convergent. The proof is constructive and we provide an algorithm to describe all such Puiseux series solutions. Moreover, we show that for any point in the complex plane there exists a solution of the differential equation which defines an analytic curve passing through this point.
PB Springer
SN 0747-7171
YR 2022
FD 2022
LK https://uvadoc.uva.es/handle/10324/64902
UL https://uvadoc.uva.es/handle/10324/64902
LA spa
NO Journal of Symbolic Computation, Volume 108, 2022, Pages 137-151,
NO Producción Científica
DS UVaDOC
RD 14-oct-2024