On the Kernel of a TwoPoint 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 twopoint 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:

 “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.springerny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 10723374
 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 TwoPoint Problem for a Partial Differential Equation of the Second Order in Time. United States: N. p., 2019.
Web. doi:10.1007/S1095801840962.
Nytrebych, Z. M., & Malanchuk, O. M. On the Kernel of a TwoPoint Problem for a Partial Differential Equation of the Second Order in Time. United States. doi:10.1007/S1095801840962.
Nytrebych, Z. M., and Malanchuk, O. M. Tue .
"On the Kernel of a TwoPoint Problem for a Partial Differential Equation of the Second Order in Time". United States. doi:10.1007/S1095801840962.
@article{osti_22773582,
title = {On the Kernel of a TwoPoint 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 twopoint 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/S1095801840962},
journal = {Journal of Mathematical Sciences},
issn = {10723374},
number = 1,
volume = 236,
place = {United States},
year = {2019},
month = {1}
}
Other availability
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.