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Integral inequalities and applications

Published online by Cambridge University Press:  17 April 2009

K. Narsimha Reddy
K. Narsimha Reddy
Affiliation:
Department of Mathematics, Osmania University, Hyderabad 500 007, India.
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Abstract

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In this paper some nonlinear analogues of Gronwall's integral inequality are established and an application to differential equations is given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 13 - 20
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Beesack, P.R., “On integral inequalities of Bihari type”, Acta Math. Acad. Sci. Hungar. 28 (1976), 31–88.CrossRefGoogle Scholar
[2]Bellman, Richard, Cooke, Kenneth L., Differential-difference equations (Mathematics in Science and Engineering, 6. Academic Press, New York, London, 1963).CrossRefGoogle Scholar
[3]Bihari, I., “A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations”, Acta Math. Acad. Sci. Hungar. 7 (1956), 81–94.CrossRefGoogle Scholar
[4]Chandra, Jagdish and Fleishman, B.A., “On a generalization of the Gronwall-Bellman lemma in partially ordered Banach spaces”, J. Math. Anal. Appl. 31 (1970), 668–681.CrossRefGoogle Scholar
[5]Chandra, J. and Lakshmikantham, V., “Some point-wise estimates for solutions of a class of nonlinear functional – integral inequalities”, Ann. Mat. Pura Appl. (4) 94 (1972), 63–74.CrossRefGoogle Scholar
[6]Dhongade, U.D. and Deo, S.G., “Some generalizations of Bellman-Bihari integral inequalities”, J. Math. Anal. Appl. 44 (1973), 218–226.CrossRefGoogle Scholar
[7]Gronwall, T.H., “Note on the derivatives with respect to a parameter of the solutions of a system of differential equations”, Ann. of Math. (2) 20 (1918–1919), 292–296.CrossRefGoogle Scholar
[8]Lakshmikantham, V. and Leela, S., Differential and integral inequalities. Volume I: Theory and applications (Mathematics in Science and Engineering, 55. Academic Press, New York and London, 1969).Google Scholar
[9]Reddy, K. Narsimha, “Existence and uniqueness problems of differential equations through inequalities” (M.Phil. dissertation, Osmania University, Hyderabad, 1979).Google Scholar
[10]Pachpatte, B.G., “Integral inequalities of Gronwall-Bellman type and their applications”, J. Math. Phys. Sci. 8 (1974), 309–318.Google Scholar
[11]Reid, William T., “Properties of solutions of an infinite system of ordinary linear differential equations of the first order with auxiliary boundary conditions”, Trans. Amer. Math. Soc. 32 (1930), 284–318.CrossRefGoogle Scholar