A retarded integral inequality and its applications. (English) Zbl 1040.26007

In the present paper retarded versions of certain integral inequalities recently established by the reviewer are given. Applications are also given to ensure the global existence of solutions to the generalized Liénard equation with delay and to a retarded Rayleigh type equation.


26D10 Inequalities involving derivatives and differential and integral operators
Full Text: DOI


[1] Bihari, I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Acad. Sci. Hungar., 7, 71-94 (1956) · Zbl 0070.08201
[2] Constantin, A., Global existence of solutions for perturbed differential equations, Ann. Mat. Pura Appl., 168, 237-299 (1995) · Zbl 0847.34008
[3] Constantin, A., Solutions globales d’équations différentielles perturbées, C. R. Acad. Sci. Paris, 320, 1319-1322 (1995) · Zbl 0839.34002
[4] Driver, R., Existence and continuous dependence of solutions of neutral functional differential equations, Arch. Rational Mech. Anal., 19, 149-166 (1965) · Zbl 0148.05703
[5] Lipovan, O., A retarded Gronwall-like inequality and its applications, J. Math. Anal. Appl., 252, 389-401 (2000) · Zbl 0974.26007
[6] Ou-Iang, L., The boundedness of solutions of linear differential equations \(y\)″+\(A(t)y=0\), Shuxue Jinzhan, 3, 409-415 (1957)
[7] Pachpatte, B. G., On some new inequalities related to certain inequalities in the theory of differential equations, J. Math. Anal. Appl., 189, 128-144 (1995) · Zbl 0824.26010
[8] Pachpatte, B. G., Inequalities for Differential and Integral Equations (1998), Academic Press: Academic Press New York · Zbl 1032.26008
[9] Souplet, P., Étude des solutions globales de certaines équations différentielles ordinaires du second ordre non linéaires, C. R. Acad. Sci. Paris, 313, 365-370 (1991) · Zbl 0738.34003
[10] Sugie, J., Continuability of solutions of the generalized Liénard system with time lag, Proc. Japan Acad., 60, 357-360 (1984) · Zbl 0567.34061
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.