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1. 7. 2000.
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)) = O, (E) extendible to infinity, follows from the oscillation of all solutions of the associated linear equation (r(t)x'(t))' + kp(t)x(t) = O, m where g(u)/u _ k or f'(u) >_ k, for every u ¢ 0 and some m, k > O. Using these results, we show that all solutions of the equilibrium capillary surface equation