We prove the existence of a sequence of solutions approach_ing zero for an elliptic system of the form -Δu = |v|~(q-2)v + g(x, v), -Δv = | u|~(p-2)u+ f (x, u) in a bounded domain, under Dirichlet homogeneous boundary conditions. We assume that 1 < p, q < 2 and that both f (x, u) and g(x, y) are small enough near the origin.
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