Abstract
Abstract In case a non-linear differential equation is reduced to a fixed-point problem, one has to apply a fixed-point theorem to a suitably chosen subset of the underlying function space. Generally speaking, in view of the non-linearity of the differential equation the restrictions for the data of the problem will be the more extensive the greater the chosen subset of the function space. The problem is to find an optimal subset leading to a domain of existence for the desired solution being as large as possible. The present paper will discuss this question for a Goursat problem.
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