Multiplicity Results for a Superlinear Elliptic System with Partial Interference with the Spectrum

In this work, we consider an elliptic system of two equations in dimension greater than one, with nonlinearities which are linear at $-\infty$ and superlinear at $+\infty$.We prove, by variational techniques which involve a strongly indefinite functional, the existence of two solutions for suitable forcing terms, under a condition on the linear part; which prevents resonance with the eigenvalues of the operator.