Abel differential equations admitting a certain first integral

Journal of Mathematical Analysis and Applications

Volumn 370, Issue 1, 2010, Pages 187-199

  Giné, Jaume ^a   Santallusia, Xavier ^a  

^a UNIVERSITY OF LLEIDA   (Spain)

Author keywords

Abel equation; Chini equation; Classical Galois theory; First integral

Indexed keywords

EID: 77953020167     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2010.04.046     Document Type: Article

References (20)

1. Appell P. Sur les invariants de quelques équations différentielles. J. Math. 1889, 5:361-423.
2. Cariñena J.F., Grabowski J., Marmo G. Superposition rules, Lie theorem, and partial differential equations. Rep. Math. Phys. 2007, 60(2):237-258.
3. Chavarriga J., Giacomini H., Giné J., Llibre J. On the integrability of two-dimensional flows. J. Differential Equations 1999, 157:163-182.
4. Chavarriga J., Giacomini H., Giné J., Llibre J. Darboux integrability and the inverse integrating factor. J. Differential Equations 2003, 194(1):116-139.
5. Cheb-Terrab E.S., Roche A.D. Abel equations: equivalence and integrable classes. Comput. Phys. Comm. 2000, 130(1-2):204-231.
6. 3. Rend. Sem. Fac. Sci. Univ. Cagliari 1940, 10:16-28.
7. Chini M. Sull'integrazione di alcune equazioni dierenziali del primo ordine. Rendiconti Instituto Lombardo 1924, 57(2):506-511.
8. Elliot Z. Sur les invariants d'une classe d'équations du premier ordre. C. R. Acad. Sci. Paris 1890, 110:629-632.
9. Françoise J.P., Roytvarf N., Yomdin Y. Analytic continuation and fixed points of the Poincare mapping for a polynomial Abel equation. J. Eur. Math. Soc. (JEMS) 2008, 10:543-570.
10. García I.A., Giacomini H., Giné J. Generalized nonlinear superposition principles for polynomial planar vector fields. J. Lie Theory 2005, 15:89-104.
11. García I.A., Giné J. Generalized cofactors and nonlinear superposition principles. Appl. Math. Lett. 2003, 16:1137-1141.
12. Giacomini H., Giné J. An algorithmic method to determine integrability for polynomial planar vector fields. European J. Appl. Math. 2006, 17(2):161-170.
13. Giné J., Llibre J. On the integrable rational Abel differential equations. Z. Angew. Math. Phys. 2010, 61(1):33-39.
14. Kamke E. Differentialgleichungen " Losungsmethoden und Losungen" Col. Math. Anwend. 1943, vol. 18. Akademische Verlagsgesellschaft Becker und Erler Kom-Ges., Leipzig.
15. Liouville R. Sur une équation différentielle du premier ordre. Acta Math.. Comptes Rendus. Comptes Rendus 1887, 103:460-463. see also R. Liouville, and R. Liouville.
16. Malgrange B. Le groupode de Galois d'un feuilletage. Monogr. Enseign. Math. 2001, vol. 38:465-501. Enseignement Math., Geneva, (in French).
17. Malgrange B. On nonlinear differential Galois theory. Chin. Ann. Math. Ser. B 2002, 23(2):219-226. dedicated to the memory of Jacques-Louis Lions.
18. λn=C. Ann. Fac. Sc. Univ. Toulouse 1896, 1-37. reprinted in Œuvres, tome 2, pp. 546-582.
19. Reid J.L., Strobel S. The nonlinear superposition theorem of Lie and Abel's differential equations. Lett. Nuovo Cimento 1983, 38(13):448-452.
20. Weisstein E.W. CRC Concise Encyclopedia of Mathematics 2003, Chapman & Hall/CRC, Boca Raton, FL. second ed.