The Exponential Property of Solutions Bounded from Below to Degenerate Equations in Unbounded Domains

This paper is focused on studying the structure of solutions bounded from below to degenerate elliptic equations with Neumann and Dirichlet boundary conditions in unbounded domains. After establishing the weak maximum principles, the global boundary Holder estimates and the boundary Harnack inequalities of the equations, we show that all solutions bounded from below are linear combinations of two special solutions (exponential growth at one end and exponential decay at the other) with a bounded solution to the degenerate equations.