Geodesic
Throughout positive solutions of second-order nonlinear differential equations
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 34C10, 34K11
Keywords: nonlinear differential equations, neutral term, eventually positive solution, throughout positive solution 
@article{EJDE_2005__2005__a34,
     author = {Zhang,  Zhenguo and Wang,  Chunjiao and Li,  Qiaoluan and Li,  Fang},
     title = {Throughout positive solutions of second-order nonlinear differential equations},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a34/}
}
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Zhang,  Zhenguo; Wang,  Chunjiao; Li,  Qiaoluan; Li,  Fang. Throughout positive solutions of second-order nonlinear differential equations. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a34/