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Solvability of a nonlinear boundary value problem without Landesman-Lazer condition. (English) Zbl 0683.34009
The author proves some existence theorems concerning the nonlinear Dirichlet boundary value problem $u''+u+f(x,u)=h(x),$ $u(0)=u(\pi)=0$, where $h\in L\sp 1[0,\pi]$ with $\int\sp{\pi}\sb{0}h(x)\sin x dx=0$ and the unbounded nonlinearity f is a Carathéodory function for $L\sp 1[0,\pi]$ satisfying certain growth conditions. The main tool is a coincidence degree result due to {\it J. Mawhin} [Topological degree methods in nonlinear BVPs, CBMS regional Conf. No.40, Am. Math. Soc. (1970)].
Reviewer: M.Goebel

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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