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Zeros of solutions of a second order nonlinear differential inequality

Author: Fu Hsiang Wong
Journal: Proc. Amer. Math. Soc. 111 (1991), 497-500
MSC: Primary 34A40; Secondary 34C10
MathSciNet review: 1034889
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Abstract: Under suitable assumptions on $ r,g$, and $ F$, we show that every zero of a solution of the nonlinear differential inequality

$\displaystyle (r(t)y'(t))' + g(t)F(y(t)) \leq 0( \geq 0)$

is simple.

References [Enhancements On Off] (What's this?)

  • [1] M. K. Kwong, Uniqueness of positive solutions of $ \Delta u - u + {u^p} = 0$ in $ {{\mathbf{R}}^n}$, Arch. Rational Mech. Anal. 105 (1989), 243-266. MR 969899 (90d:35015)
  • [2] J. P. LaSalle, Uniqueness theorems and successive approximations, Ann. of Math. 50 (1949), 722-730. MR 0031165 (11:110e)

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Keywords: Simple zero, LaSalle's inequality
Article copyright: © Copyright 1991 American Mathematical Society

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