Advances in Difference Equations
Volume 2009 (2009), Article ID 486895, 17 pages
doi:10.1155/2009/486895

An extension to nonlinear sum-difference inequality and applications

Wu-Sheng Wang1 and Xiaoliang Zhou2

1Department of Mathematics, Hechi University, Yizhou, Guangxi 546300, China
2Department of Mathematics, Guangdong Ocean University, Zhanjiang 524088, China

Abstract

We establish a general form of sum-difference inequality in two variables, which includes both more than two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities considered in the work of W.-S. Cheung (2006). Furthermore, we apply our result to a boundary value problem of a partial difference equation for boundedness, uniqueness, and continuous dependence.