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Zbl 0589.34013
Kannan, R.; Nieto, J.J.; Ray, M.B.
A class of nonlinear boundary value problems without Landesman-Lazer condition.
(English)
[J] J. Math. Anal. Appl. 105, 1-11 (1985). ISSN 0022-247X

This paper uses an abstract existence theorem of {\it L. Cesari} and the first author [Proc. Am. Math. Soc. 63, 221-225 (1977; Zbl 0361.47021)] and upper and lower solutions arguments to prove existence results for nonlinear boundary value problems of the type $-u''-u+g(u)=\cos t$, $u(0)=u(\pi)=0$ when g is bounded, nondecreasing and continuous. More general results in this direction can be found in he reviewer's monograph "Points fixes, points critique et problèmes aux limites" (1985; Zbl 0561.34001).
[J.Mawhin]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
47J05 Equations involving nonlinear operators (general)

Keywords: two-point boundary value problems; upper solutions; second order; differential equation; lower solutions

Citations: Zbl 0361.47021; Zbl 0561.34001

Cited in: Zbl 0647.49007

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