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Existence of solutions for three-point boundary value problems for second order equations


Authors: Johnny Henderson, Basant Karna and Christopher C. Tisdell
Journal: Proc. Amer. Math. Soc. 133 (2005), 1365-1369
MSC (2000): Primary 34B15; Secondary 34B10
DOI: https://doi.org/10.1090/S0002-9939-04-07647-6
Published electronically: October 18, 2004
MathSciNet review: 2111960
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Abstract: Shooting methods are employed to obtain solutions of the three-point boundary value problem for the second order equation, $y'' =f(x,y,y'),$ $y(x_1)=y_1, y(x_{3}) - y(x_2)=y_2,$ where $f: (a,b) \times \mathbb R^2 \to \mathbb R$ is continuous, $a < x_1 < x_2 < x_3 < b,$ and $y_1,y_2 \in \mathbb R,$ and conditions are imposed implying that solutions of such problems are unique, when they exist.


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Additional Information

Johnny Henderson
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
Email: Johnny_Henderson@baylor.edu

Basant Karna
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
Address at time of publication: Department of Mathematics, Marshall University, Huntington, West Virginia 25755-2560
Email: Basant_Karna@baylor.edu, karna@marshall.edu

Christopher C. Tisdell
Affiliation: School of Mathematics, The University of New South Wales, Sydney 2052, Australia
Email: cct@maths.unsw.edu.au

DOI: https://doi.org/10.1090/S0002-9939-04-07647-6
Keywords: Boundary value problem, three-point, shooting method
Received by editor(s): October 30, 2003
Received by editor(s) in revised form: December 30, 2003
Published electronically: October 18, 2004
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society

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