One system of equations with double major partial derivatives

Abstract

In particular, in [1] one establishes formulae for the integral representation of solutions to (1), characterizing their structural properties. In [7], [8] (pp. 169–191) for (1) one considers a generalization of the Goursat problem, where the desired functions enter into the boundary conditions more equitably. In addition, the qualitative character of the solvability of the proposed problem appeared to be more diverse, than that of the Goursat problem (which is uniquely solvable). The main objective of this paper is the study of a certain analog of the problem stated in [7]–[8] for the system uxx = a1(x, y)vx + b1(x, y)u + c1(x, y)v + f1(x, y), vyy = a2(x, y)uy + b2(x, y)u+ c2(x, y)v + f2(x, y). (2)