Abstract
In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation
𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢)
with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered.
Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.