We consider the initial and nonlinear oblique derivative bouodary value problem for fully nonlinear uniformly parabolic partial differential equations of second order. The parabolic operators satisfy natural structure conditions which have been introduced by Krylov. The nonlinear boundary operalors satisfy certain natural structure conditions also. The existence and uniqueness of classical solution are proved when the initial boundary values and the coefficients of the equation are suitable smooth.

We show that, for given positive parameters β and y, the Burgers-KdV equation. (1.5) has infinitely many static solutions satisfying given boundary conditions (2.1) or (3.3), and that these solutions differ from each other mainly by their numbers of extremum points.