Abstract and Applied Analysis

Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with $\Delta$-Carathéodory Functions

Abstract

We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member $f$, a $\Delta$-Carathéodory function. First, we consider the case where the nonlinearity $f$ does not depend on the $\Delta$-derivative, ${x}^{\Delta }$($t$). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems in which the nonlinearity $f$ depends on the $\Delta$-derivative and satisfies a linear growth condition with respect to ${x}^{\Delta }$($t$). Our existence results rely on notions of solution-tube that are introduced in this paper.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 234015, 26 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170948

Digital Object Identifier
doi:10.1155/2010/234015

Mathematical Reviews number (MathSciNet)
MR2771231

Zentralblatt MATH identifier
1211.34114

Citation

Frigon, M.; Gilbert, H. Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with $\Delta$ -Carathéodory Functions. Abstr. Appl. Anal. 2010 (2010), Article ID 234015, 26 pages. doi:10.1155/2010/234015. https://projecteuclid.org/euclid.aaa/1313170948