Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary

This paper is concerned with the existence and multiplicity of positive solutions of the equation - Δ u + u = up - 1, 2 < p < 2* = frac(2 N, N - 2), with Dirichlet zero data, in an unbounded smooth domain Ω ⊂ RN having unbounded boundary. Under the assumptions: (h1)∃ τ1, τ2, ..., τk ∈ R+ {set minus} {0}, 1 ≤ k ≤ N - 2, such that(x1, x2, ..., xN) ∈ Ω {long left right double arrow} (x1, ..., xi - 1, xi + τi, ..., xN) ∈ Ω, ∀ i = 1, 2, ..., k,(h2)∃ R ∈ R+ {set minus} {0} such that RN {set minus} Ω ⊂ {(x1, x2, ..., xN) ∈ RN : ∑j = k + 1N xj2 ≤ R2} the existence of at least k + 1 solutions is proved.