## Existence Theorems for Ordinary Differential EquationsTheorems stating the existence of an object—such as the solution to a problem or equation—are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations. The authors assume a basic knowledge of real function theory, and for certain specialized results, of elementary functions of a complex variable. They do not consider the elementary methods for solving certain special differential equations, nor advanced specialized topics; within these restrictions, they obtain a logically coherent discussion for students at a specific phase of their mathematical development. The treatment begins with a survey of fundamental existence theorems and advances to general existence and uniqueness theorems. Subsequent chapters explore the Picard iterants, properties of solutions, and linear differential equations. |

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Existence Theorems for Ordinary Differential Equations Francis J. Murray,Kenneth S. Miller No preview available - 2007 |

Existence Theorems for Ordinary Differential Equations Francis Joseph Murray,Kenneth S. Miller No preview available - 2012 |

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1)-dimensional euclidean space analytic Chapter complex Conclusion Consider continuous function converge uniformly convex open region Corollary corresponding defined and continuous deﬁnition dependence of solutions dependent variables dy/dx Equa Equation 14 Equation 32 euclidean space exist n functions existence and continuity exists a constant ﬁnd ﬁnite number fn(X functions y1(X fundamental system given Hence hypothesis implicit function theorem initial conditions initial point interval X0 jointly continuous Jordan normal form Lemma linear differential equation linearly independent Lipschitz condition matrix neighborhood obtain open region 21 parameters Peano existence theorem Peano theorem Picard iterants Pn(X proof prove real valued functions satisﬁes satisfy a Lipschitz satisfy Equation sequence solution of Equation speciﬁed sufﬁcient system of solutions systems of differential theory tinuous uniform convergence Wronskian X0 g X0 I g b yn(x