Abstract
where q E (0, 1) is given. We obtain conditions for the existence and uniqueness of a solution for the boundary-value problem (2), using the Leray-Schauder continuation theorem [2]. We give an example of a three-point boundary-value problem where the existence condition is not satisfied and no solution exists. Gupta [3] recently studied the boundary-value problem (2) when Q! = 1. Our results on the three-point boundary-value problem (2) extend the results of Gupta [3], to the case of general CY. (See also [4, 51.) We use the classical spaces C[O, 11, C’[O, 11, Lk[O, 11, and L”[O, l] of continuous, k-times continuously differentiable, measurable real-valued functions whose kth power of the absolute value is Lebesgue integrable on [0, 11, or measurable functions that are essentially bounded
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