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Uniqueness implies existence for fourth-order Lidstone boundary value problems. (English) Zbl 0960.34011

Summary: The uniqueness of solutions to certain boundary value problems implies their existence for the fourth-order nonlinear ordinary differential equation \(y^{(4)}= f(x,y, y',y'', y''')\). This existence is established by using shooting methods and yields results for the 2-point, 3-point, and 4-point Lidstone boundary value problems.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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