Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

Year, pages: 2009, 471 - 484

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation

$$ (r(t)(y(t)-p(t)y(t-τ))')' +q(t) G(y(h(t)) = f(t) $$

has a positive and bounded solution, where $q,h,f \in C([0,∞),\Bbb R )$ such that\linebreak $q(t) ≥ 0$, but $\not \equiv 0$, $h(t) ≤ t$, $h(t) \to ∞$ as $t \to ∞$, $r \in C⁽¹⁾([0,∞),(0,∞))$, $p \in C⁽²⁾([0,∞),\Bbb R )$, $G \in C (\Bbb R , \Bbb R )$ and $τ \in \Bbb R ⁺$. In our work $r(t) \equiv 1$ is admissible and neither we assume $G$ is non-decreasing, $xG(x) > 0$ for $x \neq 0$, nor we take $G$ is Lipschitzian. Hence the results of this paper improve many recent results.

Rath, R., Misra, N., Mishra, P. 2009. Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations. In Mathematica Slovaca, vol. 59, no.4, pp. 471-484. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0140-5

Rath, R., Misra, N., Mishra, P. (2009). Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations. Mathematica Slovaca, 59(4), 471-484. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0140-5