Problem with displacements for the three-dimensional Bianchi equation

Characteristic boundary-value problem for a system of first-order partial differential equations with shifted arguments of the desired function

“…Next, use the technique that the author applied in [12] for another problem. Namely, let us transform the integral equations to the form solved with respect to the desired function.…”

“…From [14] (P. 84) it follows that (16) has a unique solution. If we substitute this solution into (5), (12), then they will also become identities due to the equivalence of the transformations carried out. Equations themselves (5), (12) were obtained by direct integration of (1) with conditions (4) in mind.…”

“…If we substitute this solution into (5), (12), then they will also become identities due to the equivalence of the transformations carried out. Equations themselves (5), (12) were obtained by direct integration of (1) with conditions (4) in mind. So, we can one time differentiate (5) and (12) with respect to x and y, correspondingly, that will lead to identity in (1).…”

“…Equations themselves (5), (12) were obtained by direct integration of (1) with conditions (4) in mind. So, we can one time differentiate (5) and (12) with respect to x and y, correspondingly, that will lead to identity in (1). Thus, we have Theorem.…”