## Positive solutions for multi-point boundary value problem on the half-line.(English)Zbl 1110.34018

Summary: This paper presents a variety of existence results for nonlinear multipoint boundary value problems on the half-line. In particular, we consider the problem $x''(t)-px'(t)-qx(t)+f(t,x(t))=0,\quad t\in[0, \infty),$
$\alpha x(0)-\beta x'(0)-\sum^n_{i=1}k_i(\xi_i)=a, \quad \lim_{t\to\infty}\frac{x(t)}{e^{rt}}=b,\;r \in\left[0,\frac{p+\sqrt {p^2+4q}}{2}\right].$ Existence results are established using fixed-point theorems on a cone.

### MSC:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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### References:

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