On the solvability of a two point boundary value problem at resonance (Q1310478)

Let us consider the two point boundary value problem \(u''+u+g(x,u) =h(x)\) in \((0,\pi)\), \(u(0)=u(\pi)=0\), where \(h \in L^ 1(0,\pi)\) is given and \(g:(0,\pi) \times \mathbb{R} \to \mathbb{R}\) is a Carathéodory function. The solvability of this problem is studied under rather general growth restrictions on \(g\). Landesman-Lazer type sufficient conditions are considered.