Dirichlet problem with nonlinearity depending only on the derivative (Q1861870)

The authors consider the equation \(u''(t)+u(t)+g(u'(t))=f(t)\), \(t\in(0,\pi)\), together with the boundary conditions \(u(0)=u(\pi)=0,\) where \(f\) is in \(C[0,\pi]\) and \(g\) continuous and bounded. This is a resonant problem, and a Landesman-Lazer-type condition for this class of problems is not known. The authors give information on the set of functions f, for which the problem has a solution, relating it to the corresponding linear problem. This work complements a previous work by \textit{P. Drábek, P. Girg} and \textit{F. Roca} [J. Math. Anal. Appl. 257, 131-140 (2001; Zbl 0993.34012)].