BOUNDARY-VALUE PROBLEM FOR EQUATIONS WITH VARIABLE COEFFICIENTS UNSOLVABLE WITH RESPECT TO THE HIGHER TIME DERIVATIVE

摘要

In a cylindrical domain, we study the unique solvability of a boundary-value problem with data given on the whole boundary of the domain for a certain class of linear equations with partial higher-order derivatives that are unsolvable with respect to the higher time derivative with variable coefficients depending on spatial coordinates. The obtained results are transferred to the case where the equation is perturbed by a nonlinear term in the linear part.