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Positive solutions for singular three-point boundary-value problems. (English) Zbl 1142.34323

Summary: We present the Green’s function for a second-order linear differential equation with three-point boundary conditions. We give the exact expressions of the solutions for the linear three-point boundary problems by means of the Green’s function. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
34B27 Green’s functions for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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