Sums of continuous and differentiable functions in dynamical systems

We investigate stability of Martin boundaries for positive solutions of elliptic partial differential equations. We define a perturbation which isG _L ^D -semismall at infinity, show that Martin boundaries are stable under this perturbation, and give sufficient conditions for it. This work was carried out partially while the author was visiting the Department of Mathematics, Technion — Israel Institute of Technology. He wishes to thank the Israel Association for the Promotion of International Scientific Relations, the Japan Society of Promotion of Science, and the Technion.