Positive solutions for (k,n - K) conjugate multipoint boundary value problems in Banach spaces

摘要

By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem (- 1) ~(n-)k _u (n) _((t)) = f (t, u t), 0 t 1, n ≥ 2, 1 ≤ k ≤ n - 1, u (0) = ∑ _(i=1) ~(m-2)aiu (ξ i), u ~((i)) (0) = u ~((j)) (1) = θ, 1 ≤ i ≤ k - 1, 0 ≤ j ≤ n - k - 1 in a real Banach space E, where θ is the zero element of E, 0 ξ 1 ξ 2 ξ m - 2 1, a i ∈ [0, + ∞), i = 1,2, ..., m - 2. As an application, we give two examples to demonstrate our results.