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are not fulfilled. In this case the Agarwal-Kiguradze type theorems are proved which guarantee Fredholm’s property for problems (1), (2), moreover, we establish in some sense optimal, sufficient conditions for the solvability of the mentioned problem.  Consider the differential equation with deviating arguments

Figure 1 are not fulfilled. In this case the Agarwal-Kiguradze type theorems are proved which guarantee Fredholm’s property for problems (1), (2), moreover, we establish in some sense optimal, sufficient conditions for the solvability of the mentioned problem. Consider the differential equation with deviating arguments