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 ∂2u∂x2+(sgny)(1+ux2)∂2u∂y2=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.