Email this article Solution of the Cauchy problem for a degenerate second order differential equation in a Banach space
- Authors: Uskov V.I.1
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Affiliations:
- Voronezh State University of Forestry and Technologies after named G.F. Morozov
- Issue: Vol 30, No 152 (2025)
- Pages: 382-391
- Section: Original articles
- URL: https://journals.rcsi.science/2686-9667/article/view/357163
- ID: 357163
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Abstract
This article is devoted to the study of the Cauchy problem for a second-order differential equation with a non-invertible operator at the highest derivative, as a result of which, the solution exists not for every initial value. This operator is Fredholm with a zero index. The cascade splitting method is used to solve the problem. This method splits the equation and conditions into the corresponding equation and conditions in subspaces of smaller dimensions. The case of invertibility of some operator constructed by using the operator coefficients of the equation is investigated. The conditions under which a solution to the problem exists and is unique are determined; it is found in the analytical form.
About the authors
Vladimir I. Uskov
Voronezh State University of Forestry and Technologies after named G.F. Morozov
Author for correspondence.
Email: vum1@yandex.ru
ORCID iD: 0000-0002-3542-9662
Candidate of Physics and Mathematics, Senior Lecturer of the Mathematics Department
Russian Federation, 8 Timiryazeva St., Voronezh 394613, Russian FederationReferences
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