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Throughout positive solutions of second-order nonlinear differential equations. (English) Zbl 1075.34045

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
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