An Extension to Nonlinear Sum-Difference Inequality and Applications. (25th June 2009)

• Record Type: Journal Article
• Authors: Wang, Wu-Sheng; Zhou, Xiaoliang
• Other Names: Bohner Martin J. Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2009(2009)
• Publication Date: 2009-06-25
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2009/486895
• Languages: English
• ISSNs: 1687-1847

Abstract

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.