skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time

Abstract

We study the problem for a homogeneous partial differential equation of the second order with respect to time with given homogeneous two-point conditions in this variable and, in general, of the infinite order in the other (space) variable. It is proved that the analyzed problem possesses solely the trivial solution if the characteristic determinant is not identically equal to zero. In the case where the set of zeros of the characteristic determinant of this problem is nonempty, we propose a method for the construction of nontrivial solutions of the problem.

Authors:
;  [1]
  1. “L’vivs’ka Politekhnika” National University (Ukraine)
Publication Date:
OSTI Identifier:
22773582
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 236; Journal Issue: 1; Other Information: Copyright (c) 2019 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; KERNELS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; TIME DEPENDENCE

Citation Formats

Nytrebych, Z. M., and Malanchuk, O. M. On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time. United States: N. p., 2019. Web. doi:10.1007/S10958-018-4096-2.
Nytrebych, Z. M., & Malanchuk, O. M. On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time. United States. doi:10.1007/S10958-018-4096-2.
Nytrebych, Z. M., and Malanchuk, O. M. Tue . "On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time". United States. doi:10.1007/S10958-018-4096-2.
@article{osti_22773582,
title = {On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time},
author = {Nytrebych, Z. M. and Malanchuk, O. M.},
abstractNote = {We study the problem for a homogeneous partial differential equation of the second order with respect to time with given homogeneous two-point conditions in this variable and, in general, of the infinite order in the other (space) variable. It is proved that the analyzed problem possesses solely the trivial solution if the characteristic determinant is not identically equal to zero. In the case where the set of zeros of the characteristic determinant of this problem is nonempty, we propose a method for the construction of nontrivial solutions of the problem.},
doi = {10.1007/S10958-018-4096-2},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 1,
volume = 236,
place = {United States},
year = {2019},
month = {1}
}