Zhang, Zhenguo; Wang, Chunjiao; Li, Qiaoluan; Li, Fang Throughout positive solutions of second-order nonlinear differential equations. (English) Zbl 1075.34045 Electron. J. Differ. Equ. 2005, Paper No. 53, 12 p. (2005). Summary: We consider the second-order nonlinear and the nonlinear neutral functional-differential equations \[ \begin{aligned} (a(t)x'(t))'+f(t,x(g(t)))=0,&\quad t\geq t_0,\\ (a(t)(x(t)-p(t)x(t-\tau))')'+f(t,x(g(t)))=0,&\quad t\geq t_0\,. \end{aligned} \] Using Banach’s contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations. MSC: 34D05 Asymptotic properties of solutions to ordinary differential equations 34K25 Asymptotic theory of functional-differential equations 34K40 Neutral functional-differential equations Keywords:Nonlinear differential equations; neutral term; eventually positive solution; throughout positive solution PDFBibTeX XMLCite \textit{Z. Zhang} et al., Electron. J. Differ. Equ. 2005, Paper No. 53, 12 p. (2005; Zbl 1075.34045) Full Text: EuDML EMIS