Nonlinear Volterra integral equations with positive definite kernels

Staffans, Olof J.

doi:10.1090/S0002-9939-1975-0370081-8

Nonlinear Volterra integral equations with positive definite kernels
HTML articles powered by AMS MathViewer

by Olof J. Staffans PDF

Proc. Amer. Math. Soc. 51 (1975), 103-108 Request permission

Abstract:

Conditions are given for the asymptotic stability of the solution of a nonlinear Volterra integro-differential equation with convolution kernel. These conditions are less restrictive than most of the known ones for this equation.

References

Constantin Corduneanu, Sur une équation intégrale de la théorie du rélage automatique, C. R. Acad. Sci. Paris 256 (1963), 3564–3567 (French). MR 156169
A. Halanay, On the asymptotic behavior of the solutions of an integro-differential equation, J. Math. Anal. Appl. 10 (1965), 319–324. MR 176304, DOI 10.1016/0022-247X(65)90126-5
Jack K. Hale, Sufficient conditions for stability and instability of autonomous functional-differential equations, J. Differential Equations 1 (1965), 452–482. MR 183938, DOI 10.1016/0022-0396(65)90005-7
Kenneth B. Hannsgen, On a nonlinear Volterra equation, Michigan Math. J. 16 (1969), 365–376. MR 249984
J. J. Levin and J. A. Nohel, On a nonlinear delay equation, J. Math. Anal. Appl. 8 (1964), 31–44. MR 163142, DOI 10.1016/0022-247X(64)90080-0
J. J. Levin and J. A. Nohel, Perturbations of a nonlinear Volterra equation, Michigan Math. J. 12 (1965), 431–447. MR 182854
J. J. Levin and D. F. Shea, On the asymptotic behavior of the bounded solutions of some integral equations. I, II, III, J. Math. Anal. Appl. 37 (1972). MR 306849, DOI 10.1016/0022-247X(72)90258-2
Stig-Olof Londen, The qualitative behavior of the solutions of a nonlinear Volterra equation, Michigan Math. J. 18 (1971), 321–330. MR 293354
Stig-Olof Londen, On the variation of the solutions of a nonlinear integral equation, J. Math. Anal. Appl. 52 (1975), no. 3, 430–449. MR 420177, DOI 10.1016/0022-247X(75)90070-0
R. C. MacCamy and J. S. W. Wong, Stability theorems for some functional equations, Trans. Amer. Math. Soc. 164 (1972), 1–37. MR 293355, DOI 10.1090/S0002-9947-1972-0293355-X
Richard K. Miller, Asymptotic behavior of nonlinear delay-differential equations, J. Differential Equations 1 (1965), 293–305. MR 178263, DOI 10.1016/0022-0396(65)90009-4
J. A. Nohel and D. F. Shea, Frequency domain methods for Volterra equations, Advances in Math. 22 (1976), no. 3, 278–304. MR 500024, DOI 10.1016/0001-8708(76)90096-7