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Proceedings of the American Mathematical Society

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

 

 

On the boundary value problem $ u''+u=\alpha u\sp{-}+p(t),$ $ u(0)=0=u(\pi )$


Authors: L. Aguinaldo and K. Schmitt
Journal: Proc. Amer. Math. Soc. 68 (1978), 64-68
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1978-0466707-3
MathSciNet review: 0466707
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Abstract: In this note we consider the boundary value problem $ u'' + u = a{u^ - } + p(t),\;u(0) = 0 = u(\pi ),\;\alpha > 0$, and show that a necessary and sufficient condition for the problem to be solvable is that $ \smallint_0^\pi {p(s)\sin s\;ds\; \leqslant 0} $. We thus answer in the affirmative a question posed by S. Fučik.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0466707-3
Keywords: Nonlinear boundary value problems, coincidence degree theorems, continuation theorems
Article copyright: © Copyright 1978 American Mathematical Society