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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Existence and uniqueness of solutions of boundary value problems for two dimensional systems of nonlinear differential equations

Author: Paul Waltman
Journal: Trans. Amer. Math. Soc. 153 (1971), 223-234
MSC: Primary 34.36
MathSciNet review: 0268450
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Abstract: The paper considers the nonlinear system $ x' = f(t,x,y),y' = g(t,x,y)$ with linear and nonlinear two point boundary conditions. With a Lipschitz condition, an interval of uniqueness for linear boundary conditions is determined using a comparison theorem. A corresponding existence theorem is established. Under the assumption of uniqueness, a general existence theorem is established for quite general nonlinearities in the functions and in the boundary conditions. Examples are provided. The results extend previous work on second order scalar differential equations.

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Keywords: Nonlinear differential equations, boundary value problem, comparison theorem, existence and uniqueness
Article copyright: © Copyright 1971 American Mathematical Society