Nonlinear four-point problem: non-resonance with respect to the Fučík spectrum (Q838052)

The authors use ideas from their earlier work [Nonlinear Anal., Theory Methods Appl. 69, 2930--2941 (2008; Zbl 1161.34009)] to examine how the solvability of the boundary value problem \[ u''+\alpha \max (u,0)-\beta \max (-u,0)+g(u)=f\text{ on }(0,1) \] with boundary conditions \[ u'(0)=u'(\xi ),\quad u(\eta )=u(1), \] depends on the parameters \(\alpha ,\beta \in {\mathbb R}\) and \(\xi, \eta \in (0,1)\). Here, \(g\) is a sublinear continuous function and \(f\in L^1(0,1)\).