Opuscula Math. 39, no. 1 (2019), 49-60

Opuscula Mathematica

Boundary value problems with solutions in convex sets

Gerd Herzog
Peer Chr. Kunstmann

Abstract. By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.

Keywords: Dirichlet boundary value problems, solutions in convex sets, continuation method, ordered Banach spaces, concave solutions.

Mathematics Subject Classification: 34B15, 47H10.

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  • Gerd Herzog
  • Karlsruher Institut für Technologie (KIT), Institut für Analysis, D-76128 Karlsruhe, Germany
  • Peer Chr. Kunstmann
  • Karlsruher Institut für Technologie (KIT), Institut für Analysis, D-76128 Karlsruhe, Germany
  • Communicated by Jean Mawhin.
  • Received: 2018-03-29.
  • Accepted: 2018-06-21.
  • Published online: 2018-08-07.
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Cite this article as:
Gerd Herzog, Peer Chr. Kunstmann, Boundary value problems with solutions in convex sets, Opuscula Math. 39, no. 1 (2019), 49-60, https://doi.org/10.7494/OpMath.2019.39.1.49

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