All solutions of the equilibrium capillary surface equation are oscillatory Original Research Article

In this note, we show that the oscillation of all solutions of the equation extendible to infinity, follows from the oscillation of all solutions of the associated linear equation where g(u/u ≤ m, and either f(u)/u ≥ k or f′(u) ≥ k, for every u ≠ 0 and some m, k > 0. Using these results, we show that all solutions of the equilibrium capillary surface equation are oscillatory.