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Nonlinear Integral Inequalities in Two Independent Variables and Their Applications
Journal of Inequalities and Applications volume 2007, Article number: 032949 (2007)
This paper generalizes results of Cheung and Ma (2005) to more general inequalities with more than one distinct nonlinear term. From our results, some results of Cheung and Ma (2005) can be deduced as some special cases. Our results are also applied to show the boundedness of the solutions of a partial differential equation.
Pinto M: Integral inequalities of Bihari-type and applications. Funkcialaj Ekvacioj 1990,33(3):387–403.
Pachpatte BG: On some fundamental integral inequalities and their discrete analogues. Journal of Inequalities in Pure and Applied Mathematics 2001,2(2, article 15):1–13.
Pachpatte BG: On some new inequalities related to certain inequalities in the theory of differential equations. Journal of Mathematical Analysis and Applications 1995,189(1):128–144. 10.1006/jmaa.1995.1008
Lipovan O: A retarded integral inequality and its applications. Journal of Mathematical Analysis and Applications 2003,285(2):436–443. 10.1016/S0022-247X(03)00409-8
Choi SK, Deng S, Koo NJ, Zhang W: Nonlinear integral inequalities of Bihari-type without class . Mathematical Inequalities & Applications 2005,8(4):643–654.
Agarwal RP, Deng S, Zhang W: Generalization of a retarded Gronwall-like inequality and Its applications. Applied Mathematics and Computation 2005,165(3):599–612. 10.1016/j.amc.2004.04.067
Hristova SG: Nonlinear delay integral inequalities for piecewise continuous functions and applications. Journal of Inequalities in Pure and Applied Mathematics 2004,5(4, article 88):1–14.
Zhang W, Deng S: Projected Gronwall-Bellman's inequality for integrable functions. Mathematical and Computer Modelling 2001,34(3–4):393–402. 10.1016/S0895-7177(01)00070-X
Cheung W-S: Some retarded Gronwall-Bellman-Ou-Iang-type inequalities and applications to initial boundary value problems. in preparation in preparation
Dragomir SS, Kim Y-H: On certain new integral inequalities and their applications. Journal of Inequalities in Pure and Applied Mathematics 2002,3(4, article 65):1–8.
Dragomir SS, Kim Y-H: Some integral inequalities for functions of two variables. Electronic Journal of Differential Equations 2003,2003(10):1–13.
Meng FW, Li WN: On some new integral inequalities and their applications. Applied Mathematics and Computation 2004,148(2):381–392. 10.1016/S0096-3003(02)00855-X
Cheung W-S, Ma Q-H: On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications. Journal of Inequalities and Applications 2005,2005(4):347–361. 10.1155/JIA.2005.347
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Zheng, K., Wu, Y. & Deng, S. Nonlinear Integral Inequalities in Two Independent Variables and Their Applications. J Inequal Appl 2007, 032949 (2007). https://doi.org/10.1155/2007/32949
- Differential Equation
- Partial Differential Equation
- Nonlinear Term
- Integral Inequality
- General Inequality