Boundary value problems for third-order equations with discontinuous coefficient

In the work we consider boundary value problems for third order equations with changing evolution direction $\operatorname{sign}yu_{yyyy}\pm Au+c(x,y)u= f(x,y)$ in the cylinder $Q=\Omega\times(-T,T)=\{(x,y)\colon x\in\Omega,\ -T<y<T\}$, where $\Omega$ is connected subser of $\mathbb R^n$ that have smooth boundary and $T>0$. Here $A$ is elliptic operator $Au=\frac\partial{\partial x_j}\big(a^{ij}(x)u_{x_i}\big)$. It is assigned boundary conditions on lateral surface $\partial\Omega\times(-T,T)$ of cylinder $Q$ and on bases $\Omega\times\{-T\}$ and $\Omega\times\{T\}$ of cylinder for these equations. Also we assign coupling conditions on section $\Omega\times0$. We prove theorems of existence and uniquness of regular solutions of these problems.