A nonlinear generalization of Bihari’s inequality

Dhongade, U. D.; Deo, S. G.

doi:10.1090/S0002-9939-1976-0430694-2

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