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

Henderson, Johnny; Karna, Basant; Tisdell, Christopher

doi:10.1090/S0002-9939-04-07647-6

Existence of solutions for three-point boundary value problems for second order equations
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by Johnny Henderson, Basant Karna and Christopher C. Tisdell PDF

Proc. Amer. Math. Soc. 133 (2005), 1365-1369 Request permission

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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