Abstract and Applied Analysis
Volume 2012 (2012), Article ID 812165, 16 pages
http://dx.doi.org/10.1155/2012/812165
Research Article

Nonoscillatory Solutions of Second-Order Superlinear Dynamic Equations with Integrable Coefficients

Quanwen Lin1 and Baoguo Jia2

1Department of Mathematics, Maoming University, Maoming 525000, China
2School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China

Received 9 September 2011; Revised 15 November 2011; Accepted 23 November 2011

Academic Editor: D. Anderson

Copyright © 2012 Quanwen Lin and Baoguo Jia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The asymptotic behavior of nonoscillatory solutions of the superlinear dynamic equation on time scales ( 𝑟 ( 𝑡 ) 𝑥 Δ ( 𝑡 ) ) Δ + 𝑝 ( 𝑡 ) | 𝑥 ( 𝜎 ( 𝑡 ) ) | 𝛾 s g n 𝑥 ( 𝜎 ( 𝑡 ) ) = 0 , 𝛾 > 1 , is discussed under the condition that 𝑃 ( 𝑡 ) = l i m 𝜏 → ∞ ∫ 𝜏 𝑡 𝑝 ( 𝑠 ) Δ 𝑠 exists and 𝑃 ( 𝑡 ) ≥ 0 for large 𝑡 .