Second Boundary Value Problem for a Fourth-Order Inhomogeneous Equation with Variable Coefficients

The second boundary value problem in a rectangular domain for a fourth-order inhomogeneous differential equation with lower-order terms is considered. The uniqueness of the solution to the problem posed is proven by the method of energy integrals. An example is constructed for the case of violation of the conditions of the uniqueness theorem. The solution is obtained explicitly using the constructed Green’s function. Sufficient conditions for the convergence of the series and the possibility of term-by-term differentiation of this series to the required orders are obtained. The absence of a small denominator has been proven.

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