×

On the oscillation of a Volterra integral equation. (English) Zbl 0847.45003

The author studies oscillation criteria for the integral equation \[ X(t)= f(t)- \int^t_0 a(t, s) g(s, X(s)) ds,\quad t\geq 0.\tag{\(*\)} \] Sufficient conditions for all solutions of equation \((*)\) to oscillate as well as growth estimates for the solutions are given.

MSC:

45G10 Other nonlinear integral equations
45M10 Stability theory for integral equations
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] G.S. Ladde, V. Lakshmikantham and B.G. Zhang: Oscillation Theory of Differential Equations with Deviating Arguments. Marcel Dekker, Inc., New York, 1987. · Zbl 0832.34071
[2] H. Onose: On oscillation of Volterra integral equations and first order functional differential equations. Hiroshima Math. J. 20 (1990), 223-229. · Zbl 0713.45006
[3] N. Parhi and N. Misra: On oscillatory and nonoscillatory behavior of solutions of Volterra integral equations. J. Math. Anal. Appl. 94 (1983), 137-149. · Zbl 0506.45003 · doi:10.1016/0022-247X(83)90009-4
[4] B.N. Shavelo: Oscillation Theory of Functional Differential Equations with Deviating Arguments. Naukova Dumka, Kiev, 1978, pp. 133-150.
[5] B. Singh: Vanishing nonoscillations of Lienard type retarded equations. Hiroshima Math. J. 7 (1977), 1-8. · Zbl 0362.34053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.