# Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables

Oksana Malanchuk; Zinoviy Nytrebych

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 101-110
- ISSN: 2391-5455

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topOksana Malanchuk, and Zinoviy Nytrebych. "Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables." Open Mathematics 15.1 (2017): 101-110. <http://eudml.org/doc/288052>.

@article{OksanaMalanchuk2017,

abstract = {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.},

author = {Oksana Malanchuk, Zinoviy Nytrebych},

journal = {Open Mathematics},

keywords = {Null space; PDE; Two-point problem; Differential-symbol method; null space; two-point problem; differential-symbol method},

language = {eng},

number = {1},

pages = {101-110},

title = {Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables},

url = {http://eudml.org/doc/288052},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Oksana Malanchuk

AU - Zinoviy Nytrebych

TI - Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 101

EP - 110

AB - 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.

LA - eng

KW - Null space; PDE; Two-point problem; Differential-symbol method; null space; two-point problem; differential-symbol method

UR - http://eudml.org/doc/288052

ER -

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