Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales. (29th July 2010)

• Record Type: Journal Article
• Authors: Lin, Quanwen; Jia, Baoguo; Wang, Qiru
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2010(2010)
• Publication Date: 2010-07-29
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2010/294194
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We will establish a new interval oscillation criterion for second-order half-linear dynamic equation( r ( t ) [ x Δ ( t ) ] α ) Δ + p ( t ) x α ( σ ( t ) ) = f ( t ) on a time scale𝕋 which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation( [ x ′ ( t ) ] α ) ′ + c sin t x α ( t ) = cos t, whereα = p / q, p, q are odd positive integers.