Existence of Positive Solutions to Semilinear Elliptic Systems in ℝNℝN with Zero Mass

In this paper, we prove the existence of at least one positive solution pair (u, v) ∈ D1,2(ℝN) × D1,2(ℝN)(u, v) ∈ D1,2(ℝN) × D1,2(ℝN) to the following semilinear elliptic system equation(0.1){−Δu = K(x)f(v),       x∈ℝN−Δv = K(x)g(u),       x∈ℝN by using a linking theorem, where K(x  ) is a positive function in Ls(ℝN)Ls(ℝN) for some s   > 1 and the nonnegative functions f, g ∈ C(ℝ, ℝ)f, g ∈ C(ℝ, ℝ) are of quasicritical growth, superlinear at infinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual.Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problem −Δu = K(x)f(u),       x∈ℝN,−Δu = K(x)f(u),       x∈ℝN, and a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in ℝNℝN.