Oscillation theorems for second order linear differential equations with damping

Yan, Ju Rang

doi:10.1090/S0002-9939-1986-0854033-4

Oscillation theorems for second order linear differential equations with damping
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Proc. Amer. Math. Soc. 98 (1986), 276-282 Request permission

Abstract:

In this paper, we present some criteria for the oscillation of the differential equation with damping \[ (r(t)x’(t))’ + p(t)x’(t) + q(t)x(t) = 0,\quad t \in ({t_0},\infty ),\] where $p(t)$ and $q(t)$ are allowed to change sign on $[{t_0},\infty )$, and $\gamma (t) > 0$. One of our results is new even for the differential equations \[ x''(t) + q(t)x(t) = 0,\] and \[ x''(t) + p(t)x’(t) + q(t)x(t) = 0.\]

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An oscillation criterion for second-order differential equation

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