The Asymptotic Behavior of the Solutions of Some Semilinear Elliptic Equations in Cylindrical Domains

The bounded solutions of some semilinear elliptic equations in unbounded cylindrical domains are considered. Their asymptotic behavior as x → ∞ (x = coordinate along the axis of the cylinder) is analyzed and used to establish uniqueness and monotonicity in the x-variable of travelling wavefronts of some parabolic problems