Back to Search
Start Over
The nonlocal problem for the $2n$ differential equations with unbounded operator coefficients and the involution
- Source :
- Karpatsʹkì Matematičnì Publìkacìï, Vol 10, Iss 1, Pp 14-30 (2018)
- Publication Year :
- 2018
- Publisher :
- Vasyl Stefanyk Precarpathian National University, 2018.
-
Abstract
- We study a problem with periodic boundary conditions for a $2n$-order differential equation whose coefficients are non-self-adjoint operators. It is established that the operator of the problem has two invariant subspaces generated by the involution operator and two subsystems of the system of eigenfunctions which are Riesz bases in each of the subspaces. For a differential-operator equation of even order, we study a problem with non-self-adjoint boundary conditions which are perturbations of periodic conditions. We study cases when the perturbed conditions are Birkhoff regular but not strongly Birkhoff regular or nonregular. We found the eigenvalues and elements of the system $V$ of root functions of the operator which is complete and contains an infinite number of associated functions. Some sufficient conditions for which this system $V$ is a Riesz basis are obtained. Some conditions for the existence and uniqueness of the solution of the problem with homogeneous boundary conditions are obtained.
- Subjects :
- Unbounded operator
Pure mathematics
Differential equation
lcsh:Mathematics
General Mathematics
010102 general mathematics
eigenfunctions
Eigenfunction
differential-operator equation
lcsh:QA1-939
01 natural sciences
riesz basis
03 medical and health sciences
0302 clinical medicine
Operator (computer programming)
operator of involution
Periodic boundary conditions
030212 general & internal medicine
Boundary value problem
Uniqueness
0101 mathematics
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 23130210 and 20759827
- Volume :
- 10
- Database :
- OpenAIRE
- Journal :
- Carpathian Mathematical Publications
- Accession number :
- edsair.doi.dedup.....d23d650abfaa17abf0d5d05791987540