Ladas, G.; Philos, Ch. G.; Sficas, Y. G. Oscillations of integro-differential equations. (English) Zbl 0742.45003 Differ. Integral Equ. 4, No. 5, 1113-1120 (1991). 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) Cited in 1 ReviewCited in 7 Documents 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 Keywords:oscillations; integro-differential inequality; integro-differential equation; positive solution; nonlinear PDFBibTeX XMLCite \textit{G. Ladas} et al., Differ. Integral Equ. 4, No. 5, 1113--1120 (1991; Zbl 0742.45003)