Differential-symbol method of constructing the quasipolynomial solutions of a two-point problem for a partial differential equation

Abstract

We studied the solvability of a problem with local inhomogeneous conditions two-point in time for a homogeneous differential equation which is second-order in time and has generally the infinite order in spatial variables in the case where the set of zeros of the characteristic determinant of the problem is not empty and does not coincide with ℂ^s: The existence of a solution of the problem under the condition that the right-hand sides of the two-point conditions are quasipolynomials is proved. A differential-symbol method of constructing a solution of the problem is proposed.