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

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) × R 2 → R is continuous, α < x 1 < x 2 < x 3 < b, and y 1 , y 2 ∈ R, and conditions are imposed implying that solutions of such problems are unique, when they exist.

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