We study the existence and multiplicity of positive solutions to n x n systems of the form Here Δ is the Laplacian operator, λ is a non-negative parameter, Ω is a bounded domain in R~N with smooth boundary θΩ and f_i ∈ C~1 ([0, ∞)),i ∞ {1, 2,..., n}, belongs to a class of strictly increasing functions that have a combined sublinear effect at ∞. We establish results for positone systems (f_i(0) ≥ 0, i ∈ {1,...,l — 1, l +1,..., n} and f_i (0) > 0 for some l ∈ {1,... , n}), semipositone systems (no sign conditions on f_i(0)) and for systems with f_i(0) = 0, i ∈ {1, 2, ... , n}. We establish our results by the method of sub and supersolutions.
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