| Summary: | This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: $$displaylines{ y'(t) + a(t)y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), quad t in J_0, cr Delta y(t_k) = I_k(y(t_k)), quad k = 1, 2, dots , p, cr y(0) + lambda int_0^c y(s) ds = - y(c), quad lambda le 0, }$$ where $J_0 = [0, c] setminus {t_1, t_2, dots , t_p}$, $f in C(J imes mathbb{R} imes mathbb{R} imes mathbb{R}, mathbb{R})$, $I_k in C(mathbb{R}, mathbb{R})$, $a in C(mathbb{R}, mathbb{R})$ and $a(t) le 0$ for $t in [0, c]$. Sufficient conditions for the existence of coupled extreme quasi-solutions are established by using the method of lower and upper solutions and monotone iterative technique. Wang and Zhang [18] studied the existence of extremal solutions for a particular case of this problem, but their solution is incorrect.
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