OSCILLATION THEOREMS FOR 2ND-ORDER HALF-LINEAR DIFFERENTIAL-EQUATIONS

Oscillation criteria for the second-order half-linear differential equ ation [r(t)\x'(t)\(alpha-1)x'(t)]' + p(t)\x(t)\(alpha-1)x(t) = 0, t gr eater than or equal to t(0) are established, where alpha > 0 is a cons tant and integral(t)(infinity) p(s) ds exists for t is an element of [ t(0), infinity). We apply these results to the following equation: (i= 1)Sigma(N) D-i(\Du(x)\(n-2)D(i)u(x)) + c(\x\)\u(x)\(n-2)u(x) = 0, x is an element of Omega(a), where D-i = partial derivative/partial deriva tive x(i), D = (D-1,..., D-N), Omega(a) = {x is an element of IR(N) : \x\ greater than or equal to a} is an exterior domain, and asi,c is an element of C([a, infinity),IR), n > 1 and N greater than or equal to 2 are integers. Here, a > 0 is a given constant.