An Existence Result for a Linear-Superlinar Elliptic System with Neumann Boundary Conditions

In this work, we consider an elliptic system of two equations in dimension one (with Neumann boundary conditions) where the nonlinearities are asymptotically linear at $-\infty$ and superlinear at $+\infty$. We obtain that, under suitable hypotheses, a solution exists for any couple of forcing terms in $L^2$ .We also present a similar result in which the superlinearity is in only one of the two equations, and we discuss the resonant problem too.