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Existence and uniqueness for two-point boundary value problems

Published online by Cambridge University Press:  14 November 2011

John V. Baxley  and
Sarah E. Brown
John V. Baxley
Affiliation:
Mathematics Department, Wake Forest University, Winston-Salem, North Carolina, 27109, U.S.A.
Sarah E. Brown
Affiliation:
Southern Bell Telephone Company, Charlotte, North Carolina, U.S.A.
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Synopsis

Boundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 219 - 234
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

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