Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 53, pp. 1-12.
Title: Throughout positive solutions of second-order nonlinear
differential equations
Authors: Zhenguo Zhang (Hebei normal Univ., China)
Chunjiao Wang (Hebei normal Univ., China)
Qiaoluan Li (Hebei normal Univ., China)
Fang Li (Hebei normal Univ., China)
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.