Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients

UDC 517.951 We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green's function. The uniform convergence of the solutions and their derivatives contained in the equation is proved.

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