We prove that homogeneous problem for PDE of second order in time variable, and generally infinite order in spatial variables with local two-point conditions with respect to time variable, has only trivial solution in the case when the characteristic determinant of the problem is nonzero. In another, opposite case, we prove the existence of nontrivial solutions of the problem, and we propose a differential-symbol method of constructing them.
@article{bwmeta1.element.doi-10_1515_math-2017-0009,
author = {Oksana Malanchuk and Zinoviy Nytrebych},
title = {Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {101-110},
zbl = {06699452},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0009}
}
Oksana Malanchuk; Zinoviy Nytrebych. Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables. Open Mathematics, Tome 15 (2017) pp. 101-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0009/