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

Twaty A. A., Eloe P. W.

Opuscula Mathematica

2013

Vol. 33, no. 4

603--613

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.