Approximation of generalized bounded solutions of evolution equations with unbounded operator
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We substantiate a parametrization method for a differential equation in a Banach space with an unbounded operator coefficient. We propose an algorithm for finding bounded generalized solutions with an arbitrary order of accuracy.
KeywordsBanach Space Cauchy Problem Operator Matrix Bounded Solution Unbounded Operator
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- 1.V. A. Pliss, “Bounded solutions of inhomogeneous linear systems of differential equations,” in: Problems of the Asymptotic Theory of Nonlinear Oscillations [in Russian], Naukova Dumka, Kiev (1977), pp. 168–173.Google Scholar
- 2.Yu. M. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).Google Scholar
- 3.O. O. Pokutnyi, “Generalized bounded solutions of linear evolution equations in locally convex spaces,” Zh. Obchysl. Prykl. Mat., 98, No. 2, 35–40 (2009).Google Scholar
- 8.S. G. Krein, Linear Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1967).Google Scholar
- 9.V. Yu. Slyusarchuk, Stability of Solutions of Difference Equations in a Banach Space [in Ukrainian], Ukrainian National University of Water Management and Nature Resources Use, Rivne (2003).Google Scholar
- 10.L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1984).Google Scholar