A problem with inhomogeneous integral time condition for partial differential equation of first order in time and infinite order in spatial variables (Q2870369)

In this paper the authors indicate a class of quasipolynomials as a class of unique solvability of the problem with inhomogeneous integral time condition for homogeneous partial differential equation of first order in time, which, in the general case, is of infinite order in spatial variables with constant coefficients. For this class the problem solution is presented in the form of an action of a differential expression whose symbol is the right-hand side of the integral condition, onto a certain meromorphic function of parameters, which are further assumed to equal zero. In a wider class of quasipolynomials (the class of existence of non-unique solutions to the problem), a formula for constructing partial solutions of the problem is proposed.