All solutions of the equilibrium capillary surface equation are oscillatory

✍ Scribed by M.R.S. Kulenović; Ć. Ljubović

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 166 KB
• Volume: 13
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(00)00041-0

✦ Synopsis

Communicated by M. Slemrod

Abstract--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 <_ m, and either f(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 t +Bty=O, B>O, t>O, are oscillatory.