On the Dynamics of the Generalized Emden–Fowler Equation
On the Dynamics of the Generalized Emden–Fowler Equation
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广义埃姆登-福勒方程的动力学
DOI：
10.1515/gmj.2000.269
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
M. Marini
中科院分区：
文献类型：
--
作者：
M. Cecchi;Z. Došlá;M. Marini
本文给出了二阶拟线性微分方程解的定性性质的一些最新结果，其中a，B是正连续真实的函数，Φ j（u）=| u| j-2u，j > 1。在[Marini和Zezza，J. Diff. Equat. 28：1-17，1978]，我们把（1）的所有解关于它们的渐近行为分成两类。的存在性和唯一性被认为是：采用拓扑方法和半线上的边值问题相关的运营商的不动点结果。此外，还给出了一些渐近估计，并研究了当t → ∞时解收敛于零的性质.
Abstract We present some recent results dealing with the qualitative behavior of solutions of the quasilinear second order differential equation where a, b are positive continuous real functions, and Φ j (u) = |u| j–2 u, j > 1. Following a classification of solutions, proposed in the linear case in [Marini and Zezza, J. Diff. Equat. 28: 1–17, 1978], we divide all the solutions of (∗) with respect to their asymptotic behavior into two classes. The existence and uniqueness is considered: a topological approach is employed and a fixed point result for operators associated to boundary value problems on a half-line is used. In addition, some asymptotic estimates are presented and the convergence of solutions to zero as t → ∞ is studied.