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http://dx.doi.org/10.4134/JKMS.2008.45.2.331

ON SOME NEW NONLINEAR RETARDED INTEGRAL INEQUALITIES WITH ITERATED INTEGRALS AND THEIR APPLICATIONS  

Ma, Qing-Hua (DEPARTMENT OF APPLIED MATHEMATICS FACULTY OF INFORMATION SCIENCE AND TECHNOLOGY GUANGDONG UNIVERSITY OF FOREIGN STUDIES)
Pecaric, Josip (FACULTY OF TEXTILE TECHNOLOGY UNIVERSITY OF ZAGREB)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 331-353 More about this Journal
Abstract
Some new nonlinear retarded integral inequalities of Gronwall-like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No.3, pp. 563-578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.
Keywords
Gronwall-like integral inequalities; retarded; iterated integrals; priori bound;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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1 D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Mathematics and its Applications (East European Series), 53. Kluwer Academic Publishers Group, Dordrecht, 1991
2 W. S. Cheung and Q. H. Ma, Nonlinear retarded integral inequalities for functions in two independent variables, J. Concr. Appl. Math. 2 (2004), no. 2, 119-134
3 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications. Vol. I, II, Mathematics in Science and Engineering, Vol. 55-I. Academic Press, New York-London, 1969
4 M. Medved, Bihari type inequalities with multiple integral and delay, Period. Math. Hungar. 27 (1993), no. 3, 207-212   DOI
5 C. M. Dafermos, The second law of thermodynamics and stability, Arch. Rational Mech. Anal. 70 (1979), no. 2, 167-179
6 S. S. Dragomir and Y.-H. Kim, On certain new integral inequalities and their applications, JIPAM. J. Inequal. Pure Appl. Math. 3 (2002), no. 4, Article 65, 8 pp
7 S. S. Dragomir and Y.-H. Kim, Some integral inequalities for functions of two variables, Electron. J. Differential Equations (2003), no. 10, 13 pp
8 B. G. Pachpatte, Inequalities for Differential and Integral Equations, Mathematics in Science and Engineering, 197. Academic Press, Inc., San Diego, CA, 1998
9 D. Bainov and P. Simeonov, Integral Inequalities and Applications, Mathematics and its Applications (East European Series), 57. Kluwer Academic Publishers Group, Dordrecht, 1992
10 R. Bellman and K. L. Cooke, Differential-difference Equations, Academic Press, New York-London 1963
11 W. S. Cheung, Some new nonlinear inequalities and applications to boundary value problems, Nonlinear Anal. 64 (2006), no. 9, 2112-2128   DOI   ScienceOn
12 W. S. Cheung and Q. H. Ma, On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications, J. Inequal. Appl. (2005) no. 4, 347-361   DOI   ScienceOn
13 Q. H. Ma and L. Debnath, A more generalized Gronwall-like integral inequality with applications, Int. J. Math. Math. Sci. (2003), no. 15, 927-934   DOI   ScienceOn
14 F. W. Meng and W. N. Li, On some new integral inequalities and their applications, Appl. Math. Comput. 148 (2004), no. 2, 381-392   DOI   ScienceOn
15 Y. J. Cho, S. S. Dragomir, and Y.-H. Kim, On some integral inequalities with iterated integrals, J. Korean Math. Soc. 43 (2006), no. 3, 563-578   과학기술학회마을   DOI   ScienceOn
16 S. K. Choi, S. F. Deng, N. J. Koo, and W. N. Zhang, Nonlinear integral inequalities of Bihari-type without class H, Math. Inequal. Appl. 8 (2005), no. 4, 643-654
17 H. Engler, Global regular solutions for the dynamic antiplane shear problem in nonlinear viscoelasticity, Math. Z. 202 (1989), no. 2, 251-259   DOI
18 A. Haraux, Nonlinear Evolution Equations-global behavior of solutions, Lecture Notes in Mathematics, 841. Springer-Verlag, Berlin-New York, 1981
19 Q. H. Ma and J. Pecaric, Some new nonlinear retarded integral inequalities and their applications, Math. Inequal. Appl. 9 (2006), no. 4, 617-632
20 Q. H. Ma and E. H. Yang, On some new nonlinear delay integral inequalities, J. Math. Anal. Appl. 252 (2000), no. 2, 864-878   DOI   ScienceOn
21 Q. H. Ma and E. H. Yang, Some new Gronwall-Bellman-Bihari type integral inequalities with delay, Period. Math. Hungar. 44 (2002), no. 2, 225-238   DOI