Abstract
Nonlinear integral and discrete inequalities are obtained, which are related to some recent results of B. G. Pachpatte in [1] given therein as generalizations of Ou-Iang's integral inequality [2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.
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References
Bellman R, Cooke K L. Differential-Difference Equation. New York: Acad Press, 1963
Butler G, Rogers T. A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations. J Math Anal Appl, 1971, 33(1): 77–81
Ou-Iang L. The boundedness of solutions of linear differential equationy″+A(t)y=0. Shuxue Jinzhan, 1957, 1(3): 409–415.
Pachpatte B G. On some new inequalities related to certain inequalities in the theory of differential equations. J Math Anal Appl, 1995, 189(1): 128–144
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The project is supported in part by the NSF of Guangdong Province (Grnat No. 940651) and the SF of Key Discipline of the State Council Office of Overseas Chinese Affairs of China (Grant No. 93-93-6).
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Enhao, Y. On some nonlinear integral and discrete inequalitites related to Ou-Iang's inequality. Acta Mathematica Sinica 14, 353–360 (1998). https://doi.org/10.1007/BF02580438
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DOI: https://doi.org/10.1007/BF02580438