Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions
We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member f, a Δ-Carathéodory function. First, we consider the case where the nonlinearity f does not depend on the Δ-derivative, xΔ(t). We obtain existence results for Strum-Liouville and...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/234015 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member f, a Δ-Carathéodory function. First, we consider the case where the nonlinearity f does not depend on the Δ-derivative, xΔ(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 Δ-derivative and satisfies a linear growth condition with respect to xΔ(t). Our existence results rely on notions of solution-tube that are introduced in this paper. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |