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Multiple positive solutions of non-local initial value problems for first order differential systems. (English) Zbl 1245.34026
Summary: We give a new and natural method for the existence of multiple positive solutions for first order differential systems with non-local initial value conditions involving linear functionals. The case of higher order differential equations is also considered. The results are accompanied by numerical examples confirming the theory and proving for practice the importance of the bounds in solution localization.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47H11 Degree theory for nonlinear operators
34C25 Periodic solutions to ordinary differential equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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