Solution to some singular integro-differential equations II
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Abstract
In this paper we give solutions to some singular integro dierential equations of the types dydt+ a(t)Hy = f(t) (i) d2ydt2 + a(t)Hy = f(t) (ii) in the space of almost periodic functions, almost periodic distributions or semi-almost periodic distributions where a(t), b(t), and f(t) are all almost periodic functions or distributions or semi-almost periodic distributions and H is the operator of Hilbert transformations over these spaces. The equations (i) and (ii) are independent of each other and so also the coefficients a(t), b(t) and the input functions f(t). It is difficult if not impossible to find the general solutions to the above equations in terms of their coefficients and the input functions and thus it remains an open problem. We will therefore indicate the method of solving these equations by solving some specific cases which without any loss of generality will give the method of finding the general solution to the above integro-differential equations..
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