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Properties of positive solutions for \(m\)-point fractional differential equations on an infinite interval. (English) Zbl 1435.34017

In this paper, the existence and uniqueness of positive solutions is obtained, for any given parameter \(\lambda>0\), for a class of \(m\)-point fractional boundary value problems on an infinite interval \[ \begin{cases} &D^{\alpha}_{0^+}u(t)+\lambda a(t)f(t,u(t))=0, ~~ t\in (0,+\infty),\\ &u(0)=u'(0)=0, ~~ D^{\alpha-1}_{0^+}u(+\infty)=\sum_{i=1}^{m-2}\beta_iu(\xi_i) \end{cases} \] via a recent fixed point theorem for a class of generalized concave operators. Moreover, some properties of positive solutions depending on the parameter \(\lambda>0\) are given. An example illustrating the main results is also presented.

MSC:

34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
45J05 Integro-ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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