Publication result detail

TESTS FOR BOUNDEDNESS AND EXPONENTIAL STABILITY OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAYS

BEREZANSKY, L.; DIBLÍK, J.; SVOBODA, Z.; ŠMARDA, Z.

Original Title

TESTS FOR BOUNDEDNESS AND EXPONENTIAL STABILITY OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAYS

English Title

TESTS FOR BOUNDEDNESS AND EXPONENTIAL STABILITY OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAYS

Type

WoS Article

Original Abstract

Linear delayed integro-differential scalar equations with un-bounded delays x(t) +a(0)(t)x(t) +(m)Sigma(k=1)a(k)(t)x(hk(t)) +(n)Sigma(l=1)integral(t)(gl(t))Gl(t,s)x(s)ds+f(t) = 0 are considered on a semi-axis [t0,infinity),t0 is an element of R, where x(t) =phi(t) if t <= t0 and phi: (-infinity,t0]-> R. It is assumed that coefficients ak: [t0,infinity)-> R, delays hk, gl: [t0,infinity)-> R satisfying t & lowast;<= hk(t)<= t,t & lowast;<= gl(t)<= t for at & lowast;<= t0, integral kernels Gl: [t0,infinity)x[t & lowast;,infinity)-> Rand non-homogene it yf: [t0,infinity)-> Rare Lebesgue measurable functions (of one or two variables respectively). The paper derives new explicit criteria on the boundedness and exponential stability of solutions without imposing the usual restrictions of all delays and coefficients being bounded. Investigation of exponential stability is reduced to a problem of the boundedness of all solutions to an auxiliary equation. Corollaries, specific for scalar equations, are deduced from the main results. Illustrative examples are considered as well.

English abstract

Linear delayed integro-differential scalar equations with un-bounded delays x(t) +a(0)(t)x(t) +(m)Sigma(k=1)a(k)(t)x(hk(t)) +(n)Sigma(l=1)integral(t)(gl(t))Gl(t,s)x(s)ds+f(t) = 0 are considered on a semi-axis [t0,infinity),t0 is an element of R, where x(t) =phi(t) if t <= t0 and phi: (-infinity,t0]-> R. It is assumed that coefficients ak: [t0,infinity)-> R, delays hk, gl: [t0,infinity)-> R satisfying t & lowast;<= hk(t)<= t,t & lowast;<= gl(t)<= t for at & lowast;<= t0, integral kernels Gl: [t0,infinity)x[t & lowast;,infinity)-> Rand non-homogene it yf: [t0,infinity)-> Rare Lebesgue measurable functions (of one or two variables respectively). The paper derives new explicit criteria on the boundedness and exponential stability of solutions without imposing the usual restrictions of all delays and coefficients being bounded. Investigation of exponential stability is reduced to a problem of the boundedness of all solutions to an auxiliary equation. Corollaries, specific for scalar equations, are deduced from the main results. Illustrative examples are considered as well.

Keywords

FUNCTIONAL-DIFFERENTIAL EQUATIONS; CELLULAR NEURAL-NETWORKS; ASYMPTOTIC-BEHAVIOR; CONVERGENCE; SYSTEMS

Key words in English

FUNCTIONAL-DIFFERENTIAL EQUATIONS; CELLULAR NEURAL-NETWORKS; ASYMPTOTIC-BEHAVIOR; CONVERGENCE; SYSTEMS

Authors

BEREZANSKY, L.; DIBLÍK, J.; SVOBODA, Z.; ŠMARDA, Z.

Released

01.01.2025

Publisher

KHAYYAM PUBL CO INC

Location

ATHENS

ISBN

0893-4983

Periodical

Differential and Integral Equations

Volume

38

Number

1-2

State

United States of America

Pages from

43

Pages to

70

Pages count

28

URL

https://projecteuclid.org/journals/differential-and-integral-equations/volume-38/issue-1_2f_2/Tests-for-boundedness-and-exponential-stability-of-linear-integro-differential/10.57262/die038-0102-43.short

BibTex

@article{BUT198141,
  author="Leonid {Berezansky} and Josef {Diblík} and Zdeněk {Svoboda} and Zdeněk {Šmarda}",
  title="TESTS FOR BOUNDEDNESS AND EXPONENTIAL STABILITY OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAYS",
  journal="Differential and Integral Equations",
  year="2025",
  volume="38",
  number="1-2",
  pages="43--70",
  doi="10.57262/die038-0102-43",
  issn="0893-4983",
  url="https://projecteuclid.org/journals/differential-and-integral-equations/volume-38/issue-1_2f_2/Tests-for-boundedness-and-exponential-stability-of-linear-integro-differential/10.57262/die038-0102-43.short"
}