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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Existence of solutions of a nonlinear differential equation


Authors: L. Cesari and R. Kannan
Journal: Proc. Amer. Math. Soc. 88 (1983), 605-613
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1983-0702284-9
MathSciNet review: 702284
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Abstract: A criterion is proved for the existence of at least one solution to the equation $ u'' + u = g(u) + h$ with $ u(0) = u(\pi ) = 0$, where $ h \in {L_2}[0,\pi ]$ and $ g$ is continuous monotone nonincreasing.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0702284-9
Keywords: Resonance, alternative method, auxiliary and determining equations, Leray-Schauder topological argument
Article copyright: © Copyright 1983 American Mathematical Society