IMPULSIVE BOUNDARY-VALUE PROBLEMS FOR FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: y'(t) + a(t) y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), t is an element of J(0), Delta y(t(k)) = I-k(y(t(k))), k = 1, 2, ... , p, y(0) + lambda integral(c)(0) y(s)ds = -y(c), lambda <= 0, where J(0) = [0, c] \ {t(1), t(2),..., t(p)}, f is an element of C(J x R x R x R, R), I-k is an element of C(R, R), a is an element of C(R, R) and a(t) <= 0 for t is an element of [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.