Asymptotic behavior of solutions of a 2nth order nonlinear differential equation
Journal
Czechoslovak Mathematical Journal
Journal Volume
52
Journal Issue
3
Pages
665-672
Date Issued
2002
Author(s)
Abstract
In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for { (-1)nu(2n) + f(t, u) = 0, in (α, ∞), u(i)(ξ) = 0, i = 0, 1, ..., n - 1, and ξ ∈ (α, ∞), must be unbounded, provided f(t, z)z ≥ 0, in E × ℝ and for every bounded subset I, f(t, z) is bounded in E × I. (B) Every bounded solution for (-1)nu(2n) + f(t, u) = 0, in ℝ, must be constant, provided f(t, z)z ≥ 0 in ℝ × ℝ and for every bounded subset I, f(t, z) is bounded in ℝ × I.
Type
journal article