Concavity of solutions of a \(2n\)-th order problem with symmetry (Q2864636)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Concavity of solutions of a \(2n\)-th order problem with symmetry |
scientific article; zbMATH DE number 6232536
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Concavity of solutions of a \(2n\)-th order problem with symmetry |
scientific article; zbMATH DE number 6232536 |
Statements
26 November 2013
0 references
fixed-point theorems
0 references
concave and convex functionals
0 references
differential inequalities
0 references
boundary value problem
0 references
symmetry
0 references
Leggett-Williams fixed point theorem
0 references
0.8862275
0 references
0.8755644
0 references
0 references
0.87240624
0 references
0.87041223
0 references
0.86778694
0 references
0.86705637
0 references
Concavity of solutions of a \(2n\)-th order problem with symmetry (English)
0 references
In recent years, \textit{D. R. Anderson} and \textit{R. I. Avery} [J. Difference Equ. Appl. 8, No. 11, 1073--1083 (2002; Zbl 1013.47019)] have established some variants of the Leggett-Williams fixed point theorem. In this paper, one of these variants has been applied to study a two-point conjugate boundary value problem of the \(2n\)-th ordinary differential equation NEWLINE\[NEWLINE (-1)^n x^{(2n)}(t) = f(x(t)), \qquad t\in [0,1].NEWLINE\]NEWLINE In order to obtain estimates for possible solutions, the main novelty of this paper is to extend the concept of concavity to functions satisfying \(2n\)-th order differential inequalities. A a result, some sufficient conditions for the existence of solutions of the boundary value problem have been given.
0 references
