Opuscula Mathematica
Opuscula Math. 33, no. 4 (), 603-613
http://dx.doi.org/10.7494/OpMath.2013.33.4.603
Opuscula Mathematica

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



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.
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
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.