Mathematica Bohemica, Vol. 148, No. 3, pp. 303-327, 2023
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
Received November 3, 2021. Published online August 3, 2022.
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-Krasovskiǐ functional to establish our results. This work extends and improve on some results in the literature.
Keywords: boundedness; nonlinear; differential equation of third order; integral inequality
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