- 期刊
ON THE POSITIVE SOLUTIONS OF A HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH A DISCONTINUITY
並列摘要
The n-th order nonlinear functional differential equation [r(t)x^((n-υ))(t)]^((υ))=f(t,x(g(t))) is considered; necessary and sufficient conditions are given for this equation to have: (i) a positive bounded solution x(t)→B＞0 as t→∞; and (ii) all positive bounded solutions converging to 0 as t→∞. Other results on the asymptotic behavior of solutions are also given. The conditions imposed are such that the equation with a discontinuity [r(t)x^((n-υ))(t)]^((υ))=q(t)x^(-λ), λ＞0is included as a special case.
延伸閱讀
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