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A class of nonlinear boundary value problems without Landesman-Lazer condition. (English) Zbl 0589.34013
This paper uses an abstract existence theorem of 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 $-{u}^{\text{'}\text{'}}-u+g\left(u\right)=cost$, $u\left(0\right)=u\left(\pi \right)=0$ 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).
Reviewer: J.Mawhin

##### MSC:
 34B15 Nonlinear boundary value problems for ODE 47J05 Equations involving nonlinear operators (general)