TY  - JOUR
ID  - AlTwaty2013
LB  - AlTwaty2013
AU  - Al Twaty, Abdulmalik
AU  - Eloe, Paul W.
TI  - Concavity of solutions of a 2n-th order problem with symmetry
ST  - Concavity of solutions of a 2n-th order problem with symmetry
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 4
SP  - 603
EP  - 613
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.4.603
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.4.603
AB  - 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.
KW  - Fixed-point theorems
KW  - concave and convex functionals
KW  - differential inequalities
KW  - symmetry
SN  - 1232-9274
ER  -