Opuscula Math. 33, no. 4 (2013), 603-613

Opuscula Mathematica

Concavity of solutions of a 2n-th order problem with symmetry

Abdulmalik Al Twaty
Paul W. Eloe

Abstract. In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a \(2n\)-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to \(2n\)-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

Keywords: Fixed-point theorems, concave and convex functionals, differential inequalities, symmetry.

Mathematics Subject Classification: 34B15, 34B27, 47H10.

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  • Abdulmalik Al Twaty
  • University of Benghazi, Faculty of Arts & Sciences / Al Kufra, Department of Mathematics, Al Kufra, Libya
  • Paul W. Eloe
  • University of Dayton, Department of Mathematics, Dayton, Ohio 45469-2316 USA
  • Received: 2013-01-01.
  • Revised: 2013-04-13.
  • Accepted: 2013-04-13.
Opuscula Mathematica - cover

Cite this article as:
Abdulmalik Al Twaty, Paul W. Eloe, Concavity of solutions of a 2n-th order problem with symmetry, Opuscula Math. 33, no. 4 (2013), 603-613, http://dx.doi.org/10.7494/OpMath.2013.33.4.603

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