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Note on some nonlinear integral inequalities and applications to differential equations. (English) Zbl 1274.26047

Int. J. Differ. Equ. 2011, Article ID 456216, 15 p. (2011); erratum ibid. 2012, Article ID 530268, 3 p. (2012).
Summary: Using ideas from [K. Boukerrioua and A. Guezane-Lakoud, “Some nonlinear integral inequalities arising in differential equations”, Electron. J. Differ. Equ. 2008, Paper No. 80, 6 p. (2008; Zbl 1168.26307)], some nonlinear integral inequalities are established.

MSC:

26D15 Inequalities for sums, series and integrals

Citations:

Zbl 1168.26307
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References:

[1] D. Baĭnov and P. Simeonov, Integral Inequalities and Applications, vol. 57 of Mathematics and Its Applications (East European Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992. · Zbl 0912.45012
[2] B. G. Pachpatte, “On some new inequalities related to certain inequalities in the theory of differential equations,” Journal of Mathematical Analysis and Applications, vol. 189, no. 1, pp. 128-144, 1995. · Zbl 0824.26010 · doi:10.1006/jmaa.1995.1008
[3] B. G. Pachpatte, Inequalities for Differential and Integral Equations, vol. 197 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1998. · Zbl 1032.26008
[4] B. G. Pachpatte, “On some new inequalities related to a certain inequality arising in the theory of differential equations,” Journal of Mathematical Analysis and Applications, vol. 251, no. 2, pp. 736-751, 2000. · Zbl 0987.26010 · doi:10.1006/jmaa.2000.7044
[5] K. Boukerrioua and A. Guezane-Lakoud, “Some nonlinear integral inequalities arising in differential equations,” Electronic Journal of Differential Equations, vol. 2008, no. 80, pp. 1-6, 2008. · Zbl 1168.26307
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