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We study the nonlinear elliptic system of Lane–Emden type -Δ u  = sgn( v ) | v |  p -1  in Ω, -Δ v  =  f ( x , u ) in Ω,  u  =  v  = 0 on ∂Ω, where Ω is an open bounded subset of ℝ  N  ,  N  ≥ 2,  p  &gt; 1 and  f  : Ω × ℝ → ℝ is a Carathéodory function satisfying suitable growth assumptions. Existence and multiplicity results are proved by means of a generalized Weierstrass Theorem and a variant of the Symmetric Mountain Pass Theorem.

Existence and multiplicity results for some Lane–Emden elliptic systems: Subquadratic case