Abstract
In this paper, we consider a class of fractional differential equations with infinite-point boundary value conditions. Under some conditions concerning the spectral radius with respect to the relevant linear operator, both the existence of uniqueness and the nonexistence of positive solution are obtained by means of the iterative technique.
Highlights
In this paper, we consider the following fractional differential equations (FDE for short) with infinite-point boundary value conditions:⎧ ⎨Dα0+u(t) + a(t)f (t, u(t)) = 0, 0 < t < 1,⎩u(0) = u (0) = · · · = u(n–2)(0) = 0, Dβ0+u(1) = ∞ i=1 ηiDβ0+u(ξi ), (1.1)where α ≥ 2, n – 1 < α ≤ n, 0 < β < α – 1, ηi ∈ R, 0 < ξ1 < · · · < ξi < ξi+1 < · · · < 1 (i = 1, 2, . . .), ∞ i=1 ηiξiα–β = Dα0+
Liang and Zhang [9] studied the uniqueness of positive solution for the following fractional three-point Boundary value problems (BVP):
Motivated by the above works, in this paper we aim to establish the existence of uniqueness and the nonexistence of positive solution to BVP (1.1)
Summary
We consider the following fractional differential equations (FDE for short) with infinite-point boundary value conditions: In [16], the authors discussed the following fractional m-point BVP: There are few works on the uniqueness of solution for fractional boundary value problems [4, 5, 9, 17, 21, 22, 24, 26].
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