The method of sub- and super-solutions is a classical tool in the theory of second order di fferential equations. It is known that this method does not have a direct extension to almost periodic equations. We show that if an almost periodic second order semi-linear elliptic equation possesses an ordered pair of almost periodic sub- and super-solutions, then very many equations in the envelope have either almost automorphic solutions, or Besicovitch almost periodic solutions. In addition, we provide an application to almost periodically forced pendulum equations.
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