References

NOTE ON THE SINGULAR SOLUTIONS OF NONLINEAR ODES


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[2] M. Fukuda and T. Fukuda, Singular solutions of ordinary differential equations, Yokohama Math. J. 15 (1977), 45-58.

[3] D. Eisenbud and J. Harris, Schemes: The Language of Modern Algebraic Geometry, Wadsworth & Brooks/Cole Mathematics Series, 1992.

[4] E. Hille, Ordinary Differential Equations in the Complex Domain, Dover Publications Inc., 1976, Republished 1997.

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[9] P. J. Rabier and W. C. Rheinboldt, A geometric treatment of implicit differential-algebraic equations, J. of Diff. Equation 109 (1994), 110-146.

[10] H. W. Raudenbusch Jr., Ideal theory and algebraic differential equations, Trans. Am. Math. Soc. 36 (1934), 361-368.

[11] J. F. Ritt, Differential algebra, Amer. Math. Soc. Colloquium Publ. 33 (1948).

[12] J. F. Ritt, Algebraic aspects of the theory of differential equations, Amer. Math. Soc. Semi-centennial Publ. 2 (1938), 35-55.

[13] W. Sit, The Ritt-Kolchin’s theory of differential poynomials, in Differential Algebra and related topics, World Scientific (2002), 1-70.
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[14] C. N. Srinivasiengar, Singular solutions of simultaneaous ordinary differential equations, Proc. of the Indian Academy of Sciences - Section A 1(10) (1935), 668-693.

[15] R. Thom, Sur les équations différentielles multiformes et leurs integrals singulières, Boletim da Soc. Bras. De Mat., (1972), Colloque Elie Cartan, Paris 1971.

[16] H. Umemura, Galois theory and Painlevé equations, Séminaires et Congrès 14 (2006), 299-339.