Abstract :
We study the asymptotic behavior of positive solutions of the semilinear elliptic equation Δu + ƒ(u) = 0 in Ωa, u = 0 on ∂Ωa, where Ωa = {x of RN: a < x < a + 1} are expanding annuli as a → ∞, and ƒ is positive and superlinear at both 0 and ∞. We first show that there are a priori bounds for some positive solutions ua(x) as a → ∞. Then, if we fix any direction, after a suitable translation of ua the limiting solutions are non-negative solutions on the infinite strip. We can obtain more detailed descriptions of these limits if ua is radially symmetric, least-energy, or least-energy with a particular symmetry.
