A nonlinear generalization of Bihari’s inequality
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- by U. D. Dhongade and S. G. Deo PDF
- Proc. Amer. Math. Soc. 54 (1976), 211-216 Request permission
Abstract:
The aim of the present note is to prove a nonlinear generalization of the well-known integral inequality due to Bihari. This generalization is useful in obtaining pointwise estimates of solutions of nonlinear Volterra integral equations.References
- I. Bihari, Researches of the boundedness and stability of the solutions of non-linear differential equations, Acta Math. Acad. Sci. Hungar. 8 (1957), 261–278. MR 94516, DOI 10.1007/BF02020315
- Fred Brauer, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 14 (1966), 198–206. MR 192132, DOI 10.1016/0022-247X(66)90021-7
- U. D. Dhongade and S. G. Deo, Some generalizations of Bellman-Bihari integral inequalities, J. Math. Anal. Appl. 44 (1973), 218–226. MR 325892, DOI 10.1016/0022-247X(73)90039-5
- U. D. Dhongade and S. G. Deo, Pointwise estimates of solutions of some Volterra integral equations, J. Math. Anal. Appl. 45 (1974), 615–628. MR 333623, DOI 10.1016/0022-247X(74)90055-9
- D. Willett, A linear generalization of Gronwall’s inequality, Proc. Amer. Math. Soc. 16 (1965), 774–778. MR 181726, DOI 10.1090/S0002-9939-1965-0181726-3
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 211-216
- MSC: Primary 45D05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0430694-2
- MathSciNet review: 0430694