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 - Delta u + u = u(p-1), 2 < p < 2* 2N/N-2, with Dirichlet zero data, in an unbounded smooth domain Omega subset of R-N having unbounded boundary. Under the assumptions: (h(1)) there exists tau(1), tau(2),...,tau(k) is an element of R+\{0}, 1 <= k <= N - 2, such that (x(1), x(2),...,x(N)) is an element of Omega double left right arrow (x(1),...,x(i-1), x(i) + tau(i),...,x(N)) is an element of Omega, for all i = 1, 2,...,k, (h(2)) there exists R is an element of R+\{0} such that R-N\ Omega subset of {(x1, x2,...,x(N)) is an element of R-N: Sigma(N)(j=k+1) x(j)(2) <= R-2} the existence of at least k + 1 solutions is proved. (C) 2006 Elsevier Masson SAS. All rights reserved.