Oscillation criteria for second order linear differential equations with damping

Wei-Ling Liu and Horng-Jaan Li

Abstract: Some oscillation criteria are given for the second order linear differential equation with damping $$[r(t)x'(t)]'+p(t)x'(t)+q(t)x(t)=0,\quad t\geq t_0,$$ where $p(t)$ and $q(t)$ are allowed to change sign on $[t_0,\infty)$, and $r(t)>0$. These results generalize and improve some known results for the differential equations $$x''(t)+q(t)x(t)=0,$$ and $$x''(t)+p(t)x'(t)+q(t)x(t)=0.$$

Keywords: Second order differential equation with damping, oscillation,nonoscillation, generalized Riccati transformation

Classification (MSC2000): 34C10, 34C15

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