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On the existence of positive solutions for singular boundary value problems on the half-line. (English) Zbl 1185.34031

Using the fixed point theorem for completely continuous operators in cones, the authors prove the existence of positive solutions of the following singular problem: \[ \begin{aligned} \dfrac{1}{p(t)}(p(t)z'(t))'&+\mu f(t,z(t),z'(t))=0, \quad t\in (0,\infty),\\ a_1z(0)&-b_1\lim_{t\to 0^+}p(t)z'(t)=0, \\ a_2\lim_{t\to \infty}z(t)&+b_2\lim_{t\to\infty}p(t)z'(t)=0. \end{aligned} \]

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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References:

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