On the resonance problem with nonlinearity which has arbitrary linear growth (Q1101596)

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.