@Article{AlTwaty2013,
author = "Al Twaty, Abdulmalik and Eloe, Paul W.",
title = "Concavity of solutions of a 2n-th order problem with symmetry",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "4",
pages = "603--613",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.4.603",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.4.603",
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",
issn = "1232-9274"
}