Xuyang Fu, Zhijuan Gao, Qiaoluan Li. SOME GENERALIZED GRONWALL-LIKE RETARDED INEQUALITIES IN TWO INDEPENDENT VARIABLES ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 339-353. doi: 10.11948/2014018
Citation: |
Xuyang Fu, Zhijuan Gao, Qiaoluan Li. SOME GENERALIZED GRONWALL-LIKE RETARDED INEQUALITIES IN TWO INDEPENDENT VARIABLES ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 339-353. doi: 10.11948/2014018
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SOME GENERALIZED GRONWALL-LIKE RETARDED INEQUALITIES IN TWO INDEPENDENT VARIABLES ON TIME SCALES
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College of Mathematics and Information Science, Hebei Normal University, Nan Er Huan Dong Lu. No 20, Hebei Shijiazhuang 050024, China
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Abstract
In this paper, we establish some new Gronwall-like inequalities in two independent variables which can be used as tools in the theory of integral equations with delay on time scales.
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References
[1]
|
R. Bellman, The Stability of solutions of linear differential equations, Duke Math. J., 10(1934), 643-647.
Google Scholar
|
[2]
|
M. Bohner and A. Peterson, Dynamic Equations on Time Scale:An Introduction with Applications, Birkhäuser, Boston, 2001.
Google Scholar
|
[3]
|
Q. H. Feng and B. Zheng, Generalized Gronwall-Bellman-type delay dynamic inequalities on time scales and their applications, Appl. Math. Comput., 218(2012), 7880-7892.
Google Scholar
|
[4]
|
Rui A. C. Ferreria and Delfim F. M. Torres, Generalized retarded integral inequalities, Appl. Math. Lett, 22(2009), 876-881.
Google Scholar
|
[5]
|
T. H. Gronwall, Note on the derivatives with respect to a parameter of solution of a system of defferential equations, Ann. Math., 20(1919), 231-237.
Google Scholar
|
[6]
|
F. C. Jiang and F. W. Meng, Explicit bounds on some new nonlinear integral inequality with delay, J. Comput. Appl. Math., 205(2007), 479-486.
Google Scholar
|
[7]
|
W. N. Li, Some intergral useful in the theory of certain partail dynamic equations on time scales, Comput. Math. Appl.,61(2011), 1754-1759.
Google Scholar
|
[8]
|
O. Lipovan, A retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl., 25(2000), 389-401.
Google Scholar
|
[9]
|
Q. H. Ma and E. H. Yang, Some new Gronwall-Bellman-Bihari type integral inequalities with delay, Period. Math. Hungar., 44(2)(2002), 225-238.
Google Scholar
|
[10]
|
R. Xu and Y. G. Sun, On retarded integral inequalities in two independent variables and their applications, Appl. Math. Comput., 182(2006), 1260-1266.
Google Scholar
|
[11]
|
H. P. Ye and J. M. Gao, Henry-Gronwall type retarded integral inequalities and their applications to fractional differential equations with delay, Appl. Math. Comput., 218(2011), 4152-4160.
Google Scholar
|
[12]
|
H. X. Zhang and F. W. Meng, On certain integral inequalities in two independent variables for retarded equations, Appl. Math. Comput., 203(2008), 608-616.
Google Scholar
|
-
-
-