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Sbornik: Mathematics, 2010, Volume 201, Issue 8, Pages 1193–1215
DOI: https://doi.org/10.1070/SM2010v201n08ABEH004109 (Mi sm7562) 		 
This article is cited in 22 scientific papers (total in 22 papers)

The method of local linear approximation in the theory of nonlinear functional-differential equations

V. E. Slyusarchuk

Ukranian State Academy of Water Economy
English version PDF (405 kB) Citations (22)
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DOI: https://doi.org/10.1070/SM2010v201n08ABEH004109
Abstract: Conditions for the existence of solutions to the nonlinear functional-differential equation
$$ \frac{d^mx(t)}{dt^m}+(Fx)(t)=h(t), \qquad t\in\mathbb R, $$
in the space of functions bounded on the axes are obtained by using local linear approximation to the operator $F$.
Bibliography: 21 items.
Keywords: functional-differential equations, invertibility of nonlinear operators.
Received: 20.03.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 8, Pages 103–126
DOI: https://doi.org/10.4213/sm7562
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 34C11, 47J05
Language: English
Original paper language: Russian
Citation: V. E. Slyusarchuk, “The method of local linear approximation in the theory of nonlinear functional-differential equations”, Mat. Sb., 201:8 (2010), 103–126; Sb. Math., 201:8 (2010), 1193–1215
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    • This publication is cited in the following 22 articles:
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    English version PDF:9
    References:76
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