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

We study the nonlinear elliptic system of Lane–Emden type -Δu = sgn(v) |v|p-1 in Ω, -Δv = f(x,u) in Ω, u = v = 0 on ∂Ω, where Ω is an open bounded subset of ℝN, N ≥ 2, p > 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