Solution of the Boundary Value Problem for a Third Order Equation with Little Terms. Construction of the Green's Function

The paper considers the first boundary value problem in a rectangular domain for a third-order inhomogeneous equation with lower-order terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The solution is written out in terms of the constructed Green's function. In justifying the uniform convergence of the solution, a non-zero value of the "small denominator" is set.