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On the solvability of two-point in time problem for PDE. (English) Zbl 1391.35005

Summary: We prove that the solution of problem for homogeneous partial differential equation of the second order in time variable in which nonhomogeneous local two-point conditions are given, and infinite order in spatial variables, may not exist in the class of entire functions in the case when the characteristic determinant of the problem equals zero identically. In the case of existence of the solution of the problem, we propose the formula of finding its particular solutions.

MSC:

35A01 Existence problems for PDEs: global existence, local existence, non-existence
35G05 Linear higher-order PDEs
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