Nytrebych, Z. M.; Malanchuk, O. M. On the kernel of two-point problem for second order time partial differential equation. (Ukrainian, English) Zbl 1399.35136 Mat. Metody Fiz.-Mekh. Polya 59, No. 3, 43-54 (2016). 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. Reviewer: L. N. Chernetskaja (Kyïv) MSC: 35G05 Linear higher-order PDEs 35G10 Initial value problems for linear higher-order PDEs Keywords:initial problem with two-point conditions; existence of quasipolynomial solutions PDFBibTeX XMLCite \textit{Z. M. Nytrebych} and \textit{O. M. Malanchuk}, Mat. Metody Fiz.-Mekh. Polya 59, No. 3, 43--54 (2016; Zbl 1399.35136)