Generalized solutions of algebraic differential equations
نویسندگان
چکیده
منابع مشابه
Solutions of Algebraic Differential Equations
This paper may be considered as a mathematical essay on the question “What is a solution of an algebraic differential equation?” Many theorems in differential algebra are proved by differentiating an algebraic differential equation several times, and then eliminating certain quantities, say, by the use of resultants. We give the simplest example of this, that every C” solution of an ADE satisfi...
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The Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing pcurvatures for almost all p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on P1−{0, 1,∞}. We prove a variant of this conjecture for P1−{0, 1,∞}, which asserts that if the equation satisfies a certain conve...
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Nonsmooth equation-solving and optimization algorithms which require local sensitivity information are extended to systems with nonsmooth parametric differential-algebraic equations embedded. Nonsmooth differential-algebraic equations refers here to semi-explicit differential-algebraic equations with algebraic equations satisfying local Lipschitz continuity and differential right-hand side func...
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where F is a polynomial in the first k+ 1 variables, whose coefficients are analytic functions of the independent variable z. If the conditions of Cauchy's theorem for the existence and uniqueness of the solution are satisfied, then (0.1) determines an analytic function in a neighbourhood of a given point z0. One of the most difficult problems in the analytic theory of differential equations is...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1986
ISSN: 0022-0396
DOI: 10.1016/0022-0396(86)90100-2