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

Author(s): Abdulmalik Al Twaty | Paul W. Eloe

Journal: Opuscula Mathematica
ISSN 1232-9274

Volume: 33;
Issue: 4;
Start page: 603;
Date: 2013;
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Keywords: Fixed-point theorems | concave and convex functionals | differential inequalities | symmetry

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.

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