On a New Nonlinear Sum-difference Inequality with Application

Authors: Kelong Zheng, Shouming Zhong

Abstract:

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given.

Keywords: Sum-Difference inequality, Nonlinear, Boundedness.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329751

References:

[1] W. S. Cheung, Q. H. Ma, J. Peˇcari'c, Some discrete nonlinear inequalities and applications to difference equations, Acta Mahtematica Scientia 2008, 28B(2) 417-430.
[2] W. S. Cheung, J. Ren, Discrete non-linear inequalities and applications to boundary value problems, J. Math. Anal. Appl. 319 (2006) 708-724.
[3] S. Deng, Nonlinear discrete inequalities with two variables and their applications, Appl. Math. Comput. (2010), doi:10.1016/j.amc.2010.07.022.
[4] F. C. Jiang, F. W. Meng, Explicit bounds on some new nonlinear integral inequalities with delay, J. Comput. Appl. Math. 205(2007), 479-486.
[5] Y. H. Kim, On some new integral inequalities for functions in one and two variables, Acta Math. Sinica, 2(2)(2005), 423-434.
[6] O. Lipovan, A retarded integral inequality and its applications, J. Math. Anal. Appl. 285(2003), 436-443.
[7] Q. H. Ma, W. S. Cheung, Some new nonlinear difference inequaities and their applications, Journal of Computational and Applied Mathematics 202(2007), 339-351.
[8] B. G. Pachpatte, Inequalities for Finite Difference Equations, Marcel Dekker, New York, 2002.
[9] Y. Wu, X. Li, S. Deng, Nonlinear delay discerte inequalities and their applications to Voliterra type difference equations, Advances in Difference Equations, Volumn 2010, Aritcle ID 795145, 14 pages.
[10] K. Zheng, Some retarded nonlinear integral inequalities in two variables and applications, JIPAM. J. Inequal. Pure Appl. Math. 9(2)(2008), Article 57, 11 pp.