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Positive solutions for singular boundary value problems of a coupled system of differential equations. (English) Zbl 1076.34022
The authors study existence conditions for multiple positive solutions on a particular two-point boundary value problem for a system of two nonlinear ordinary differential equations, one of order 4 and the other one of order 2, with singularities in the right-hand sides and possible applications in civil construction engineering. Under appropriate assumptions, first, the existence of at least one positive solution is established and, second, the existence of at least two positive solutions is also established by means of a fixed-point theorem of cone expansion and compression. The utility of the approach is illustrated by three concrete examples.
MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE