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Zbl 0683.34009
Santanilla, Jairo
Solvability of a nonlinear boundary value problem without Landesman-Lazer condition.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 13, No.6, 683-693 (1989). ISSN 0362-546X

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)].
[M.Goebel]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE

Keywords: Landesman-Lazer condition; nonlinear Dirichlet boundary value problem; Carathéodory function; coincidence degree

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