Multiplicity results for some perturbed elliptic problems in unbounded domains with non-homogeneous boundary conditions

We study the following nonlinear elliptic problem {−Δu+mu=g(x,u)+f(x)in  RN∖B¯R,u=hon  ∂BR,u→0as  ∣x∣→+∞, with N≥3N≥3, m∈R+∗, under suitable conditions on the radial functions gg, ff and hh. Multiplicity results are proved in the perturbed case f≢0f≢0 and h≢0h≢0 by using Bolle’s perturbation method and suitable growth estimates on min–max critical levels.