Abstract In this paper, we study real solutions of the nonlinear Helmholtz equation − Δ u − k 2 u = γ M (x) | u | q − 2 u + f (x, u) for x ∈ R N, -u-k^2u= M (x) u ^q-2u+f (x, u) \, for\, x R^N, subject to the asymptotic conditions u (x) = O | x | 1 − N 2 and ∂ 2 u ∂ r 2 (x) + k 2 u (x) = o | x | 1 − N 2, as r = | x | → ∞, u (x) =O (x ^1-N{2}) and ^{2u} {r^2} (x) +k^2u (x) =o (x ^1-N{2}), as\, r= x, where N ≥ 1, k > 0, q ∈ (1, 2). Assuming that f (x, t</jats: i
Chen et al. (Thu,) studied this question.