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Positive solutions for three-point boundary value problem on the half-line. (English) Zbl 1131.34019
Summary: We consider the existence of positive solutions for the following boundary value problem on the half-line
\[ \begin{cases} (\rho(t)x'(t))'+f(t,x(t),x'(t))=0,\quad & t\in [0,+\infty),\\ x(0)=\alpha x(\xi),\quad \lim_{t\to\infty}x(t)=0.\end{cases} \] By applying fixed-point theorems, we obtain a variety of existence results. In particular, the nonlinear term is involved with the first-order derivative.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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