Spatially Nonlocal Problems with Integral Conditions for Ultraparabolic Equation

The article is devoted to investigating the solvability of new nonlocal boundary value problems for linear ultraparabolic equations with two time variables and one spatial variable. The main peculiarities of the problems is first that nonlocal conditions of integral form are given with respect to the spatial variable and second, that the coefficient at one of the time derivatives may degenerate. The article aims to prove existence and uniqueness theorems for regular solutions, i.e., or solutions having all weak derivatives in the sense of S. L. Sobolev occurring in the equation.