文章基本信息

标题：On the positive solutions of a higher order functional differential equation with a discontinuity
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作者：John R. Graef ; Paul W. Spikes ; Myron K. Grammatikopoulos 等
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1982
卷号：5
DOI：10.1155/S0161171282000234
出版社：Hindawi Publishing Corporation
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.