Skip to main content
SpringerLink
Log in

Conditions for the Existence of Nonoscillating Solutions of Nonlinear Differential Equations with Delay and Pulse Influence in a Banach Space

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For nonlinear differential second-order equations with delay and pulse influence in a Banach space, we establish necessary and sufficient conditions for the existence of their solutions nonoscillating with respect to a subspace.

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. V. Yu. Slyusarchuk, “Oscillation of solutions of differential and differential-difference equations in a Banach space,” in: Nonlinear Differential Equations and Their Applications [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993), pp. 66-70.

    Google Scholar 

  2. V. Yu. Slyusarchuk, “Oscillation of solutions of differential equations with pulse action a Banach space,” in: Constructive Methods for the Investigation of Differential Equations [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993), pp. 174-178.

    Google Scholar 

  3. V. Yu. Slyusarchuk, “Sufficient conditions for the oscillation of the trajectories of impulsive systems with nonfixed times of pulse action,” in: Integral Transformations and Their Applications to Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1994), pp. 192-197.

    Google Scholar 

  4. V. Yu. Slyusarchuk, “Oscillation of solutions of the difference equation ?2 x(n) + ? mk=1 Pk(n)gk(x(n))= 0 in a Banach space,” in: Systems of Evolution Equations with Aftereffect [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995), pp. 98-102.

    Google Scholar 

  5. V. Yu. Slyusarchuk, “Oscillation of solutions of differential equations in a Banach space,” in: Proceedings of International Mathematical Conference Dedicated to the Memory of H. Hahn, Ruta, Chernivtsi (1995), pp. 269-275.

  6. V. Yu. Slyusarchuk, “Necessary and sufficient conditions for the oscillation of solutions of nonlinear differential equations with pulse action a Banach space,” Ukr. Mat. Zh., 51, No. 1, 98-109 (1999).

    Google Scholar 

  7. R. R. Ushakov and V. I. Khatset, Convex Functions and Inequalities [in Ukrainian], Vyshcha Shkola, Kiev (1986).

    Google Scholar 

  8. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  9. L. Nirenberg, Topics in Nonlinear Functional Analysis, New York University, New York (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shevchenko Kiev University, Kiev

    M. O. Perestyuk

  2. Rivne Technical University, Rivne

    V. Yu. Slyusarchuk

Authors
  1. M. O. Perestyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Yu. Slyusarchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perestyuk, M.O., Slyusarchuk, V.Y. Conditions for the Existence of Nonoscillating Solutions of Nonlinear Differential Equations with Delay and Pulse Influence in a Banach Space. Ukrainian Mathematical Journal 55, 956–965 (2003). https://doi.org/10.1023/B:UKMA.0000010595.59886.57

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000010595.59886.57

Keywords

Search

Navigation