“…(4), (5), (10), (11), (14), and (15) and the assumption of the smoothness of the functions λ ij are satisfied, the functions f i are continuous in all arguments, continuously differentiable with respect to x, y, and u, and satisfying the global Lipschitz condition with respect to u n ∈R uniformly in ( , , ) x y t ∈ M for every compact set M ∈Π , and the functions ϕ i and μ i are continuously differentiable. Then problem (1), (2), (12) has a unique classical solution in the domain Π .…”