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Reproducing kernel method for singular fourth order four-point boundary value problems. (English) Zbl 1219.34032
The authors consider singular fourth order linear ordinary differential equations with boundary conditions stating that the solution equals zero at four specified points. Analytical approximate solutions in the form of convergent series are obtained by means of a reproducing kernel.

MSC:
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
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