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Matematicheskie Zametki, 2018, Volume 103, Issue 1, Pages 75–91
DOI: https://doi.org/10.4213/mzm11312
(Mi mzm11312)
 

Generalization of the Lagrange Method to the Case of Second-Order Linear Differential Equations with Constant Operator Coefficients in Locally Convex Spaces

S. N. Mishin

Orel State University named after I. S. Turgenev
References:
Abstract: The well-known Lagrange method for linear inhomogeneous differential equations is generalized to the case of second-order equations with constant operator coefficients in locally convex spaces. The solutions are expressed in terms of uniformly convergent functional vector-valued series generated by a pair of elements of a locally convex space. Sufficient conditions for the continuous dependence of solutions on the generating pair are obtained. The solution of the Cauchy problem for the equations under consideration is also obtained and conditions for its existence and uniqueness are given. In addition, under certain conditions, the so-called general solution of the equations (a function of most general form from which any particular solution can be derived) is obtained. The study is carried out using the characteristics (order and type) of an operator and of a sequence of operators. Also, the convergence of operator series with respect to equicontinuous bornology is used.
Keywords: locally convex space, order and type of an operator, operator-differential equation, equicontinuous bornology, bornological convergence, vector-valued function.
Received: 18.07.2016
Revised: 24.01.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 1, Pages 75–88
DOI: https://doi.org/10.1134/S0001434618010091
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
Citation: S. N. Mishin, “Generalization of the Lagrange Method to the Case of Second-Order Linear Differential Equations with Constant Operator Coefficients in Locally Convex Spaces”, Mat. Zametki, 103:1 (2018), 75–91; Math. Notes, 103:1 (2018), 75–88
Citation in format AMSBIB
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