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Multiple positive solutions of multi-point boundary value problems on the half-line. (English) Zbl 1136.34026

From the introduction: We establish the existence of positive solutions to the following multi-point boundary value problems on the half-line:
\[ \begin{cases} x''(t)-k^2x(t)+m(t)f(t,x(t))+h(t)g(t,x(t))=0,\quad 0<1<+\infty,\\ x(0)=\sum^{m-2}_{i=1}\alpha_ix(\xi_i),\quad \lim_{t\to\infty}x(t)=0,\end{cases} \tag{1} \]
by applying the fixed-point theorem of cone expansion and compression type due to Krasnosel’skii in a special function space.

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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References:

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