The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′...The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ<SUB> i </SUB>∈ (0, 1) with 0 【 ξ<SUB>1</SUB> 【 ξ<SUB>2</SUB> 【 · · · 【 ξ<SUB> m−2</SUB> 【 1, a <SUB>i </SUB>∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions.展开更多
文摘The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ<SUB> i </SUB>∈ (0, 1) with 0 【 ξ<SUB>1</SUB> 【 ξ<SUB>2</SUB> 【 · · · 【 ξ<SUB> m−2</SUB> 【 1, a <SUB>i </SUB>∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions.
