THE NEUMANN BOUNDARY VALUE PROBLEM FOR A SEMILINEAR ELLIPTIC EQUATION IN A THIN CYLINDER. THE LEAST ENERGY SOLUTIONS

摘要

It is proved that the least energy solution of the, BVPrn{-Δu+u = |u|~(q-2)u in Q, au/an = 0 on aQ.rnis a constant for all q ∈ (2; 2~*] if Q is contained in R~n (n ≥ 3) is a sufficiently thin cylinder.