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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.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
Full Text: DOI
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