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Oscillations of integro-differential equations. (English) Zbl 0742.45003

The integro-differential inequality (1) \(\dot y(t)+\int^ t_ 0 K(t- s)y(s)ds\leq 0\), \(t\geq T\) and the corresponding integro-differential equation (2) \(\dot y(t)+\int^ t_ 0 K(t-s)y(s)ds=0\), \(t\geq T\) are considered. Sufficient conditions, under which no positive solution of (1) exists, and necessary and sufficient conditions for existence of a positive solution of equation (2) are established. The results obtained are extended to the nonlinear case.
Reviewer: H.D.Voulov (Sofia)

MSC:

45J05 Integro-ordinary differential equations
45M20 Positive solutions of integral equations
26D10 Inequalities involving derivatives and differential and integral operators
45G10 Other nonlinear integral equations
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