This paper deals with an elliptic system of the form in Ω, in Ω, on ∂ Ω, where is a parameter and ( ) is a bounded domain with -boundary ∂ Ω, (a bounded open interval if ). Here with a.e. in Ω and are constants. The nonlinear perturbations are Caratheodory functions that are sublinear at infinity. We provide sufficient conditions for determining the λ-direction to which a continuum of positive and negative solutions emanates from infinity at the first eigenvalue of the associated linear problem. Furthermore, as a consequence of main results, we also provide sufficient condition for the solvability of a class of asymptotically linear system near and at resonance satisfying Landesman-Lazer type conditions. MSC: 35J60.