Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams; Mathew O. Omeike; Idowu A. Osinuga; Biodun S. Badmus

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 3, page 303-327
  • ISSN: 0862-7959

Abstract

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We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results. This work extends and improve on some results in the literature.

How to cite

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Adams, Daniel O., et al. "Boundedness criteria for a class of second order nonlinear differential equations with delay." Mathematica Bohemica 148.3 (2023): 303-327. <http://eudml.org/doc/299116>.

@article{Adams2023,
abstract = {We consider certain class of second order nonlinear nonautonomous delay differential equations of the form \[ a(t)x^\{\prime \prime \} + b(t)g(x,x^\prime ) + c(t)h(x(t-r))m(x^\prime ) = p(t,x,x^\prime ) \] and \[ (a(t)x^\prime )^\prime + b(t)g(x,x^\prime ) + c(t)h(x(t-r))m(x^\prime ) = p(t,x,x^\prime ), \] where $a$, $b$, $c$, $g$, $h$, $m$ and $p$ are real valued functions which depend at most on the arguments displayed explicitly and $r$ is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results. This work extends and improve on some results in the literature.},
author = {Adams, Daniel O., Omeike, Mathew O., Osinuga, Idowu A., Badmus, Biodun S.},
journal = {Mathematica Bohemica},
keywords = {boundedness; nonlinear; differential equation of third order; integral inequality},
language = {eng},
number = {3},
pages = {303-327},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness criteria for a class of second order nonlinear differential equations with delay},
url = {http://eudml.org/doc/299116},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Adams, Daniel O.
AU - Omeike, Mathew O.
AU - Osinuga, Idowu A.
AU - Badmus, Biodun S.
TI - Boundedness criteria for a class of second order nonlinear differential equations with delay
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 3
SP - 303
EP - 327
AB - We consider certain class of second order nonlinear nonautonomous delay differential equations of the form \[ a(t)x^{\prime \prime } + b(t)g(x,x^\prime ) + c(t)h(x(t-r))m(x^\prime ) = p(t,x,x^\prime ) \] and \[ (a(t)x^\prime )^\prime + b(t)g(x,x^\prime ) + c(t)h(x(t-r))m(x^\prime ) = p(t,x,x^\prime ), \] where $a$, $b$, $c$, $g$, $h$, $m$ and $p$ are real valued functions which depend at most on the arguments displayed explicitly and $r$ is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results. This work extends and improve on some results in the literature.
LA - eng
KW - boundedness; nonlinear; differential equation of third order; integral inequality
UR - http://eudml.org/doc/299116
ER -

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