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On the resonance problem with nonlinearity which has arbitrary linear growth. (English) Zbl 0642.34009

This paper deals with the nonlinear two-point boundary value problem at resonance of the form \(u''+u+g(x,u)=h(x),\) \(u(0)=u(\pi)=0\), where \(h\in L^ 1(0,\pi)\) and g is a Caratheodory function. It is shown that also nonlinearity g with an arbitrary linear growth at \(+\infty\) (resp. - \(\infty)\) but with the corresponding bound on their linear growth at - \(\infty\) (resp. \(+\infty)\) may be considered. The solvability of the problem is proved.
Reviewer: P.Chocholatý

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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