Electron. J. Diff. Eqns., Vol. 2005(2005), No. 53, pp. 1-12.

Throughout positive solutions of second-order nonlinear differential equations

Zhenguo Zhang, Chunjiao Wang, Qiaoluan Li, Fang Li

Abstract:
In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations
$$\displaylines{ (a(t)x'(t))'+f(t,x(g(t)))=0,\quad t\geq t_0\cr (a(t)(x(t)-p(t)x(t-\tau))')'+f(t,x(g(t)))=0,\quad t\geq t_0\,. }$$
Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.

Submitted December 13, 2004. Published May 19, 2005.
Math Subject Classifications: 34C10, 34K11.
Key Words: Nonlinear differential equations; neutral term; eventually positive solution; throughout positive solution.

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Zhenguo Zhang
College of Mathematics and Information Science
Hebei normal University
Heibei, Shijiazhuang, 050016, China
email: Zhangzhg@mail.hebtu.edu.cn
Chunjiao Wang
College of Mathematics and Information Science
Hebei normal University
Heibei, Shijiazhuang, 050016, China
email: ccjjj0601@sina.com.cn
Qiaoluan Li
College of Mathematics and Information Science
Hebei normal University
Heibei, Shijiazhuang, 050016, China
email: qll71125@163.com
Fang Li
College of Mathematics and Information Science
Hebei normal University
Heibei, Shijiazhuang, 050016, China
email: lifanglucky@126.com

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