Abstract
The condition of acyclicity of the solution set of the Cauchy problem for an ordinary differential equation can be used in the theory of boundary value problems.
However, the acyclicity of a funnel does not imply the acyclicity of sections of the funnel for a fixed time. There exist acyclic integral funnels whose time sections are not acyclic. In the present paper, we show that there is a relationship in the reverse direction: the acyclicity of time sections of integral funnels implies the acyclicity of the funnels themselves. This fact can simplify the application of existence theorems for boundary value problems to specific equations.
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Original Russian Text © I.I. Turko, V.V. Filippov, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 2, pp. 271–273.
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Turko, I.I., Filippov, V.V. On the acyclicity of integral funnels. Diff Equat 45, 279–281 (2009). https://doi.org/10.1134/S0012266109020177
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DOI: https://doi.org/10.1134/S0012266109020177