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Proceedings of the American Mathematical Society

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On the existence of positive solutions of ordinary differential equations


Authors: L. H. Erbe and Haiyan Wang
Journal: Proc. Amer. Math. Soc. 120 (1994), 743-748
MSC: Primary 34B15; Secondary 47N20
DOI: https://doi.org/10.1090/S0002-9939-1994-1204373-9
MathSciNet review: 1204373
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Abstract: We study the existence of positive solutions of the equation $ {u^{''}} + a(t)f(u) = 0$ with linear boundary conditions. We show the existence of at least one positive solution if $ f$ is either superlinear or sublinear by a simple application of a Fixed Point Theorem in cones.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1204373-9
Keywords: Boundary value problems, positive solution, superlinear and sublinear, fixed point theorem in cones
Article copyright: © Copyright 1994 American Mathematical Society