On some nonlinear boundary-value problems in cylindrical domains

The paper deals with a linear elliptic second-order equation in divergent form in a semi-infinite cylinder Ω =Ω x [0, ∞), where Ω is a bounded domain, Ω ⊂ ℝn-1 0 ≤ xn < ∞ The solution under consideration satisfies the nonlinear boundary condition, ∂u/∂v+ao|u|q-1 u= 0, where ∂/∂v is the differentiation along the external conormal a0 = const > 0, q = const. The asymptotic behavior of the solution for xn → +∞ is studied. Bibliography: 15 titles. © 1997 Plenum Publishing Corporation.