A class of nonlinear boundary value problems without Landesman-Lazer condition (Q1073993)

This paper uses an abstract existence theorem of \textit{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).