On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations

Journal of Differential Equations - Tập 263 - Trang 7099-7122 - 2017
A. Cima1, A. Gasull1, F. Mañosas1
1Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

Tài liệu tham khảo

Bayat, 2005, An extension of ABC-theorem, Sci. Magna, 1, 81 Bhargava, 1964, Degrees of polynomial solutions of a class of Ricatti-type differentials equation, Collect. Math., 16, 211 Bhargava, 1965, Existence of polynomial solutions of a class of Ricatti-type differentials equation, Collect. Math., 17, 135 Bhargava, 1966, Some properties of polynomial solutions of a class of Ricatti-type differentials equation, Collect. Math., 18, 3 Bombieri, 1991, The generalized Fermat equation in function fields, J. Number Theory, 39, 339, 10.1016/0022-314X(91)90053-E de Bondt Campbell, 1952, A criterion for the polynomial solutions of a certain Ricatti equation, Amer. Math. Monthly, 59, 388, 10.2307/2306810 Campbell, 1952, On the polynomial solutions of a Ricatti equation, Amer. Math. Monthly, 61, 402 Fulton, 1969 Gasull, 2016, The number of polynomial solutions of polynomial Ricatti equations, J. Differential Equations, 261, 5071, 10.1016/j.jde.2016.07.019 Gine, 2013, On the polynomial limit cycles of polynomial differential equations, Israel J. Math., 106, 481 Hartshorne, 1977, Algebraic Geometry, vol. 52 Huffstutler, 1972, Criterion for the polynomial solutions of certain first order differential equations, Port. Math., 31, 139 Lemmermeyer, 2012, Parametrization of algebraic curves from a number theorist's point of view, Amer. Math. Monthly, 119, 573, 10.4169/amer.math.monthly.119.07.573 Mason, 1984, Diophantine Equations over Functions Fields, vol. 96 Newman, 1979, Waring's problem for the ring of polynomials, J. Number Theory, 11, 477, 10.1016/0022-314X(79)90027-1 Pinter, 1992, Exponential diophantine equations over function fields, Publ. Math. Debrecen, 41, 89, 10.5486/PMD.1992.1167 Ragot, 2002, Probabilistic absolute irreducibility test for polynomials, J. Pure Appl. Algebra, 172, 87, 10.1016/S0022-4049(01)00165-7 Rainville, 1936, Necessary conditions for polynomial solutions of certain Ricatti equations, Amer. Math. Monthly, 43, 473, 10.1080/00029890.1936.11987882 Shapiro, 1994, Extension of a theorem of Mason, Comm. Pure Appl. Math., XLVII, 711, 10.1002/cpa.3160470506 Silverman, 1984, The S-unit equation over function fields, Math. Proc. Cambridge Philos. Soc., 95, 3, 10.1017/S0305004100061235 Stothers, 1981, Polynomial identities and Hauptmodulen, Quart. J. Math. Oxford Ser. (2), 32, 349, 10.1093/qmath/32.3.349