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Existence of positive solutions to vector boundary value problems II. (English) Zbl 0967.34012
This paper is the second part of the author’s work on the existence of positive solutions to second-order vector differential systems with Dirichlet boundary value conditions. A sufficient condition on definition intervals was proved in the first part of the paper [Math. Slovaca 49, No. 4, 453-479 (1999; Zbl 0952.34017)] that guarantees the existence of a positive solution to the system. This paper gives a necessary condition on the definition intervals for the existence of a positive solution to the system. There are also presented simple assumptions on the nonlinearities of the system establishing a necessary and sufficient condition for the existence of a positive solution to such system.
MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:
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