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We prove a Phragmen-Lindelof theorem which yields the behavior at infinity of bounded solutions of Dirichlet problems for non-hyperbolic (e.g., elliptic, parabolic) quasilinear second-order partial differential equations in terms of particular solutions of appropriate ordinary differential equations.

A Phragmèn–Lindelöf theorem and the behavior at infinity of solutions of non-hyperbolic equations