Detail publikačního výsledku

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

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

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

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

Vydáno

01.01.2025

Nakladatel

KHAYYAM PUBL CO INC

Místo

ATHENS

ISSN

0893-4983

Periodikum

Differential and Integral Equations

Svazek

38

Číslo

1-2

Stát

Spojené státy americké

Strany od

43

Strany do

70

Strany počet

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"
}