Let be a bounded domain in the space of points with an integer, and let have the boundary . Denote , , , and , and assume that all functions are real-valued. In , consider the equation
where , , ; and , ; ; and , ; , ; (the summation convention is used, with summation over repeated indices from 1 to .
Equation (1) is elliptic, parabolic, or hyperbolic at a point , if , , or . Since no restrictions are imposed on the sign of in , (1) is of mixed type.
The following nonlocal problem is investigated: to find a solution of (1) in such that
where and .
Further it is assumed that . The author continues earlier studies [Differ. Uravn. 23, No. 1, 78-84 (1987; Zbl 0648.35059)] and establishes other sufficient conditions ensuring that (1), (2) has a unique generalized solution, and investigates its smoothness.