Archive of Issues
Russia Tambov
Section  Mathematics 
Title  Comparison of solutions to boundaryvalue problems for linear functionaldifferential equations 
Author(s)  Zhukovskiy E.S.^{a}, Takhir Kh.M.^{a} 
Affiliations  Tambov State University^{a} 
Abstract  We consider the issues of solvability of boundary value problems for linear functionaldifferential equations. Statements allowing one to obtain conditions for the existence of a unique solution and for nonnegativity of the Green's function, and to obtain a fundamental solution to the homogeneous equation are suggested. In order to apply these statements, one needs to define a “reference” boundary value problem that possesses the corresponding properties and to define an operator by means of the operators generated by the problem under study and the “reference” problem according to the given rule. If the spectral radius of this operator is less than 1, then the boundary value problem under consideration is uniquely solvable. Similarly, in order to obtain conditions for the nonnegativity of the Green's function and the fundamental solution, it is required to determine a special operator by the rule given in the paper and to verify its positivity. An example of application of the statements obtained to a particular boundary value problem with an integral boundary condition for the equation containing argument deviations to the unknown function and to its derivative is considered. 
Keywords  linear functionaldifferential equation, boundary value problem, Green's function, fundamental solution of a homogeneous equation, positive operator 
UDC  517.977 
MSC  34K10, 34K06 
DOI  10.20537/vm180302 
Received  27 April 2018 
Language  Russian 
Citation  Zhukovskiy E.S., Takhir Kh.M. Comparison of solutions to boundaryvalue problems for linear functionaldifferential equations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 3, pp. 284292. 
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