On the existence of solutions for a system of difference equations with non-monotone nonlinearity (Q654238)

In this short note the author is concerned with a nonlinear equation of the form \[ Au = \lambda f(u), \quad u \in \mathbb R^N \] arising from a nonlinear difference equation with boundary conditions. \(f\) is assumed to be a \(C^1\) function, that relaxes the condition from an earlier result by the author [J. Difference Equ. Appl. 16, No. 1, 121--124 (2010; Zbl 1198.39014)] that the components of \(f\) are nondecreasing. The author determines by a dual variational method, for which values of \(\lambda\) solutions of the above equation exist.