Asymptotic properties of solutions of semilinear second-order elliptic equations in cylindrical domains.

The equations under consideration have the following structure: where 0 < x _n < ∞, ( x ₁, ..., x _n−1) ∈ Ω, Ω is a bounded Lipschitz domain, $$f(0,x_n ) \equiv 0,\tfrac{{\partial f}}{{\partial u}}(0,x_n ) \equiv 0$$ is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations as x _n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas were obtained in the case of a _ij, a_i depending only on ( x ₁, ..., x _n−1). [ABSTRACT FROM AUTHOR]