Resonant nonlinear boundary value problems with almost periodic nonlinearity (Q1420731)

The authors describe the set of continuous functions \(h\) for which the problem \[ -u''(x)- u(x)+ g(u(x))= h(x), \quad x\in [0,\pi], \qquad u(0)= u(\pi)= 0, \] has a solution. They assume \(g\) to be continuous and bounded, with an assumption on the primitive \(g\) which is satisfied, for example, when \(g\) is almost-periodic.