THE DISTANCE BETWEEN ZEROS OF AN OSCILLATORY SOLUTION TO A HALF-LINEAR DIFFERENTIAL-EQUATION

Consider the oscillatory equation (\u'(t)\(alpha-1)u'(t))'+q(t)\u(t)\( alpha-1)u(t) = 0 where q(t) : [a, infinity) --> R is locally integrabl e for some a greater than or equal to 0. We prove some results; on the distance between consecutive zeros of a solution of (). We apply als o the results to the following (t)\u'(t)\(alpha-1)u'(t))'+q(t)\u(t)\(a lpha-1)u(t) = 0 and [GRAPHICS] where (i) r epsilon C([0, infinity),(0, infinity)) and integral(a)(infinity)r(t)(-1/alpha)=infinity; (ii) D-i = partial derivative/partial derivative x(i), D = (D-1, ..., D-N); Om ega(a) = {x epsilon R(N) : \x\ greater than or equal to a} is an exter ior domain, and c epsilon C([a, infinity), [0, infinity)); (iii) alpha > 0; n > 1 and N greater than or equal to 2.