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 greater than or equal to 0, where p(t) and q(t) are continuous and periodic. The results show that the equation y{''} + (sint)y' + (cost)y = 0 is nonoscillatory whilst the equation y{''} + (cost)y' + (sint)y = 0 is oscillatory. (C) 2003 Elsevier Inc. All rights reserved.