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Operator Theory, Pseudo-Differential Equations, and Mathematical Physics pp 275–292Cite as

Birkhäuser

Almost Periodic Elliptic Equations: Sub- and Super-solutions

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 228))

Abstract

The method of sub- and super-solutions is a classical tool in the theory of second-order differential 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.

Mathematics Subject Classification (2010). Primary 35B15; Secondary 35J15, 34C27, 34C15.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD, 21251, USA

    Gaston M. N’Guérékata & Alexander Pankov

Authors
  1. Gaston M. N’Guérékata
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  2. Alexander Pankov
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Corresponding author

Correspondence to Gaston M. N’Guérékata .

Editor information

Editors and Affiliations

  1. de Morelos, Facultad de Ciencias, Universidad Autónoma del Estado, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, 62209, Morelos, Mexico

    Yuri I. Karlovich

  2. , Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino, 10123, Italy

    Luigi Rodino

  3. , Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Straße 39, Chemnitz, 09126, Germany

    Bernd Silbermann

  4. , Department of Mathematics, College of William and Mary, Jones Hall 114, Williamsburg, 23187-8795, Virginia, USA

    Ilya M. Spitkovsky

Additional information

Dedicated to Professor Vladimir Rabinovich on the occasion of his 70th Birthday

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N’Guérékata, G.M., Pankov, A. (2013). Almost Periodic Elliptic Equations: Sub- and Super-solutions. In: Karlovich, Y., Rodino, L., Silbermann, B., Spitkovsky, I. (eds) Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. Operator Theory: Advances and Applications, vol 228. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0537-7_14

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