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A GOURSAT-TYPE PROBLEM FOR A HIGH ORDER PARTIAL DIFFERENTIAL EQUATION

0. Introduction Goursat-type boundary value problems for hyperbolic partial differential equations of orders greater than two in rectangular domains have been examined in papers [1], [2], [4] and [9]-[ll] (see also the references therein). One of the most fundamental assumptions in all these papers is that the curves considered in the problem do not intersect one another except one vertex of the rectangle. In this paper we consider a Goursat-type problem in the case when the said curves additionally meet at the opposite vertex of the rectangle which makes the problem overdetermined and hence much harder. We examine it by using the method given by Fichera [5] and then applied by the present author [3] in a more complicated case. Let us observe that also the differential operator appearing in the considered equation and the boundary conditions dealt with in the paper are more general than those in the earlier papers (cf. Remark 1.1 in the sequel).