Some equations with partial derivative of high order

In this article are a boundary problems for linear and non linear equation with partial derivative of order higher than two considered. For some conditions on coefficients of equation are proven an uniqueness and existence theorems. If conditions on coefficients differential equation are not fulfilled or changed of boundary conditions then given a examples solutions these problems, which will be non uniquely, non stable and will not belong to Sobolev space. Moreover, also given a exactly solutions for equations of Korteweg–de Vries, Kadomzeva–Petviashwili.