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

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

Mathematica Bohemica, Tome 148 (2023) no. 3, pp. 303-327

Abstract (VO)

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\v ı functional to establish our results. This work extends and improve on some results in the literature.

Détail

DOI : 10.21136/MB.2022.0166-21

Classification : 34C11, 34C12, 34K12
Keywords: boundedness; nonlinear; differential equation of third order; integral inequality

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