Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions. (12th December 2010)

• Record Type: Journal Article
• Authors: Frigon, M.; Gilbert, H.
• Other Names: Mawhin J. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2010(2010)
• Publication Date: 2010-12-12
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2010/234015
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right memberf, aΔ -Carathéodory function. First, we consider the case where the nonlinearityf does not depend on theΔ -derivative, x Δ (t ). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems in which the nonlinearityf depends on theΔ -derivative and satisfies a linear growth condition with respect tox Δ (t ). Our existence results rely on notions of solution-tube that are introduced in this paper.