The Tricomi problem for a genuinely nonlinear Lavrentiev–Bitsadze equation of mixed type

In this paper, we consider the Tricomi problem for a genuinely nonlinear Lavrentiev–Bitsadze mixed-type equation ∂ 2 u ∂ x 2 + ( sgn y ) ( 1 + u x 2 ) ∂ 2 u ∂ y 2 = 0 , whose coefficients depend on the first-order derivative of an unknown function. We prove the existence of a solution to this problem by a method which can be used to study more difficult problems for nonlinear mixed-type equations arising in gas dynamics.