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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
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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
[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
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