Skip to main content
SpringerLink
Log in

Stieltjes Differential in Impulse Nonlinear Problems

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. A. M. Savchuk, Izv. Math. 82 (2), 351–376 (2018).

    Article  MathSciNet  Google Scholar 

  2. A. S. Ivanov and A. M. Savchuk, Math. Notes 102 (2), 164–180 (2017).

    Article  MathSciNet  Google Scholar 

  3. N. N. Konechnaya, K. A. Mirzoev, and A. A. Shkalikov, Math. Notes 104 (2), 244–252 (2018).

    Article  MathSciNet  Google Scholar 

  4. A. M. Savchuk and A. A. Shkalikov, Funct. Anal. Appl. 44 (4), 270–285 (2010).

    Article  MathSciNet  Google Scholar 

  5. P. B. Dzhakov and B. S. Mityagin, Russ. Math. Surv. 61 (4), 663–766 (2006).

    Article  Google Scholar 

  6. V. A. Mikhailets, Funct. Anal. Appl. 30 (2), 144–146 (1996).

    Article  MathSciNet  Google Scholar 

  7. Yu. V. Pokornyi, Dokl. Math. 59 (1), 34–37 (1999).

    Google Scholar 

  8. Yu. V. Pokornyi, Dokl. Math. 65 (2), 262–265 (2002).

    Google Scholar 

  9. F. V. Atkinson, Discrete and Continuous Boundary Problems (Academic, New York, 1964).

    MATH  Google Scholar 

  10. Yu. V. Pokornyi, M. B. Zvereva, and S. A. Shabrov, Russ. Math. Surv. 63 (1), 109–153 (2008).

    Article  Google Scholar 

  11. Yu. V. Pokornyi, Zh. I. Bakhtina, M. B. Zvereva, and S. A. Shabrov, Sturm’s Oscillation Method in Spectral Problems (Fizmatlit, Moscow, 2009) [in Russian].

    MATH  Google Scholar 

Download references

Funding

This work was supported by the Ministry of Education and Science of the Russian Federation (project no. 14.Z50.31.0037) and by the Russian Science Foundation (project no. 19-11-00197) and was performed at Voronezh State University (Theorems 1–4).

Author information

Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    A. D. Baev, D. A. Chechin, M. B. Zvereva & S. A. Shabrov

Authors
  1. A. D. Baev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Chechin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. B. Zvereva
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. A. Shabrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. D. Baev, M. B. Zvereva or S. A. Shabrov.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baev, A.D., Chechin, D.A., Zvereva, M.B. et al. Stieltjes Differential in Impulse Nonlinear Problems. Dokl. Math. 101, 5–8 (2020). https://doi.org/10.1134/S1064562420010111

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562420010111

Keywords:

Search

Navigation