Abstract. This paper contains sufficient conditions under which there exist extremal solutions of initial value problems for delay integro-differential equations of mixed type in Banach spaces. We use the monotone iterative technique for proving existence results. Some comparison results are also established.
2000 Mathematics Subject Classification. 45J05, 34G20.
Key words and phrases. Delay integro-differential equations, lower and upper solutions, monotone sequences, convergence, extremal solutions.