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On the kernel of two-point problem for second order time partial differential equation. (Ukrainian, English) Zbl 1399.35136

The authors study a problem for homogeneous second order time partial differential equation. With respect to the time variable two-point conditions are given, which are of generally infinite order with respect to another (spatial) variable. The problem is proved to have a trivial solution only if the characteristic determinant of the problem is not identically zero. In the case when the characteristic determinant set of zeros is non-empty, a method for constructing nontrivial solutions of the problem is proposed.

MSC:

35G05 Linear higher-order PDEs
35G10 Initial value problems for linear higher-order PDEs
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