Oscillation and nonoscillation of Hill’s equation with periodic damping

We prove new results on the oscillation and nonoscillation of the Hill’s equation with periodic damping: y + p(t)y +q(t)y = 0, t 0, where p(t) and q(t) are continuous and periodic. The results show that the equation y +(sin t)y + (cos t)y = 0 is nonoscillatory whilst the equation y + (cos t)y + (sin t)y = 0 is oscillatory.  2003 Elsevier Inc. All rights reserved.