All solutions of the equilibrium capillary surface equation are oscillatory

doi:10.1016/S0893-9659(00)00041-0

Applied Mathematics Letters

Volume 13, Issue 5, July 2000, Pages 107-110

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Abstract

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.