Title  Periodic solutions of a quartic differential equation and Groebner bases 
Author(s)  Mohamed A. M. Alwash 
Type  Article in Journal 
Abstract  We consider firstorder ordinary differential equations with quartic nonlinearities. The aim is to find the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. It is shown that this number is ten when the coefficients are certain cubic polynomials. Equations with the maximum number of such periodic solutions are also constructed. The paper is heavily dependent on computing Groebner bases. 
Keywords  nonlinear differential equations, periodic solutions, multiplicity, bifurcation, Groebner bases, MAPLE 
Length  10 
ISSN  03770427 
File 

URL 
dx.doi.org/10.1016/S03770427(96)000593 
Language  English 
Journal  Journal of Computational and Applied Mathematics 
Volume  75 
Number  1 
Pages  6776 
Publisher  Elsevier Science Publishers B. V. 
Address  Amsterdam, The Netherlands, The Netherlands 
Year  1996 
Month  November 
Edition  0 
Translation 
No 
Refereed 
No 