All solutions of the equilibrium capillary surface equation are oscillatory

In this note, we show that the oscillation of all solutions of the equation [r(t)g (y'(t))]' + p(t)f(y(t)) = 0, extendible to infinity, follows from the oscillation of all solutions of th e associated linear equation [r(t)x' (t)]' + k/mp(t)x(t) = 0, where g(u)/u less than or equal to m, and either f(u)/u greater than or equ al to k or f'(u) greater than or equal to k, for every u not equal 0 and so me m, k > 0. Using these results, we show that all solutions of the equilib rium capillary surface equation (t y'/root 1 + y'(2))' + Bty = 0, B > 0, t > 0, are oscillatory. (C) 2000 Elsevier Science Ltd. All rights reserved.