A perturbation result of semilinear elliptic equations in exterior strip domains

In this paper we show that if the decay of nonzero fis fast enough, then the perturbation Dirichlet problem -Delta u + u = u(p) + f(z) in Omega has at least two positive solutions, where N = m+n, m greater than or equal to 3, n greater than or equal to 1, 1 < p < N+2/N-2, omega subset of R-m a bounded C-1,C-1 domain S = omega x R-n, D is a bounded C-1,C-1 domain in Rm+n such that D subset of subset of S and Omega = S\D. In case f equivalent to 0, we assert that there is a positive higher-energy solution providing that D is small.