**AUTHORS:**Dalila Bitat, Hassane Khellaf

**Download as PDF**

**ABSTRACT:**
In this paper, we present some non-linear integral inequalities with a term of delay for functions of two
independent variables that can be used in the theory of differential and integral equations with time delay. Also,
we generalize these inequalities by integration over infinite intervals. An application is given as an illustration

**KEYWORDS:**
Non-linear integral inequalities with delay; Two independent variables; Non-decreasing functions;
Differential and integral equations with delay; Integration over infinite intervals

**REFERENCES:**

[1] Boudeliou, A., and H. Khellaf. On some delay non-linear integral inequalities in two independent variables. Journal of Inequalities and Applications. No. 313, 2015.

[2] Ghrissi, T., and M. A. Hammami. Generalized retarded integral inequalities of Gronwall type and applications. WSEAS Transactions on Mathematics. Vol. 16, 2017, pp. 173-182.

[3] Jiang, F. C., and F. W. Meng. Explicit bounds on some new non-linear integral inequality with delay. Journal of Computational and Applied Mathematics. No. 205, 2007, pp. 479-487.

[4] Khellaf, H., and M. Smakdji. Nonlinear delay integral inequalities for multi-variable functions. Electronic Journal of Differential Equations. No. 169, 2011, pp. 1-14.

[5] Mi, Y. Some generalized Gronwall-Bellman type impulsive integral inequalities and their applications. Journal of Applied Mathematics. 2014.

[6] Pachpatte, B.G. On a certain retarded integral inequality and its applications. Journal of Inequalities in Pure and Applied Mathematics. Vol. 5, No. 1, 2004.

[7] Qingling, G., and Q. Zhonghua. A generalized retarded Gronwall-like inequalities. Applied Mathematical Sciences. Vol. 7, No. 99, 2013, pp. 4943-4948.

[8] Xu, R., and X. Ma. Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications. Journal of Inequalities and Applications. No. 187, 2017.

[9] Zhang, H., and F. Meng. Integral inequalities in two independent variables for retarded Volterra equations. Applied Mathematics and Computation. No. 199, 2008, pp. 90-98.