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- Title
Stieltjes Differential in Impulse Nonlinear Problems.
- Authors
Baev, A. D.; Chechin, D. A.; Zvereva, M. B.; Shabrov, S. A.
- Abstract
An impulse nonlinear problem admitting discontinuous solutions that are functions of bounded variation is studied. This problem models the deformation of a discontinuous string (chains of strings fastened together by springs) with elastic supports in the form of linear and nonlinear springs (for example, springs with different turns, whose deformations do not obey Hooke's law). The model is described by a second-order differential equation with derivatives in special measures and Dirichlet boundary conditions. Existence theorems are proved, and conditions for the existence of nonnegative solutions are obtained.
- Subjects
NONLINEAR equations; FUNCTIONS of bounded variation; EXISTENCE theorems; STIELTJES integrals; DIFFERENTIAL equations; DIRICHLET principle
- Publication
Doklady Mathematics, 2020, Vol 101, Issue 1, p5
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562420010111