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Nonlinear Discrete Inequalities of Bihari-type and Applications

Nonlinear Discrete Inequalities of Bihari-type and Applications
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摘要 Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illustrate the boundedness of solutions of a difference equation are also given. Discrete Bihari-type inequalities with n nonlinear terms are discussed, which generalize some known results and may be used in the analysis of certain problems in the theory of difference equations. Examples to illustrate the boundedness of solutions of a difference equation are also given.
作者 Yu WU
机构地区 College of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第3期603-614,共12页 应用数学学报（英文版）
基金 Supported by the Program of Education Department of Sichuan Province(No.10ZA173)
关键词 discrete inequality Bihari’s type NONLINEAR MONOTONICITY discrete inequality Bihari’s type nonlinear monotonicity
分类号 O178 [理学—基础数学] O175.26 [理学—基础数学]
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  • 1Agarwal, R.P. On an integral inequality in n independent variables. J. Math. Anal. Appl., 85:192-196 (1982).
  • 2Agarwal, R.P., Deng, S., Zhang, W. Generalization of a retarded Gronwall-like inequality and its applica- tions. Appl. Math. Comput., 165:599-612 (2005).
  • 3Bihari, I. A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta Math. Acad. Sci. Hungar., 7:81-94 (1956).
  • 4Borysenko, S., Matarazzo, G., Pecoraro, M. A generalization of Bihari's lemma for discontinuous functions and its application to the stability problem of differential equations with impulse disturbance. Georgian Math. J., 13:229-238 (2006).
  • 5Cheung, W. Gronwall-Bellman-Bihari integral inequalities and application to nonlinear Volterra integral equation. Southeast Asian Bull. Math., 29:447-454 (2005).
  • 6Choi, S.K., Deng, S., Koo, N.J., Zhang, W. Nonlinear integral inequalities of Bihari-type without class H. Math. Inequal. AppI., 8:643-654 (2005).
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  • 8Horvath, L. Generalizations of special Bihari type integral inequalities. Math. Inequal. Appl., 8:441-449 (2005).
  • 9Lungu, N. On some Gronwall-Bihari-Wendorff-type inequalities. Semin. Fixed Point Theory C1uj-Napoca, 3:249-254 (2002).
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Acta Mathematicae Applicatae Sinica
2013年 第3期

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