Existence of solutions for first order singular problems

Cherpion, Marielle;De Coster, C
(2000) Proceedings of the American Mathematical Society — Vol. 128, n° 6, p. 1779-1791 (2000)

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Abstract
We develop the lower and upper solutions method for first order initial value problems as well as for first order periodic problems in case the nonlinearity presents singularities. More precisely we prove that if we have a lower solution alpha and an upper solution beta of these problems, which are not necessarily continuous nor ordered, we have a solution wedged between min{alpha, beta} and max{alpha, beta}.
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Cherpion, M., & De Coster, C. (2000). Existence of solutions for first order singular problems. Proceedings of the American Mathematical Society, 128(6), 1779-1791. https://doi.org/10.1090/S0002-9939-99-05515-X (Original work published 2000)