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Existence of solutions for three-point boundary value problems for second order equations
Authors:Johnny Henderson   Basant Karna   Christopher C. Tisdell
Affiliation:Department of Mathematics, Baylor University, Waco, Texas 76798-7328 ; Department of Mathematics, Baylor University, Waco, Texas 76798-7328 ; School of Mathematics, The University of New South Wales, Sydney 2052, Australia
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.

Keywords:Boundary value problem   three-point   shooting method
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