关键词: 正解, 非线性 $n$ 阶时滞微分方程, 锥不动点定理, 边界值问题, Semipositone 问题 , 正解, 非线性 $n$ 阶时滞微分方程, 锥不动点定理, 边界值问题, Semipositone 问题

Abstract: This paper dealt with the existence of positive solutions
for the nonlinear eigenvalue problem and the superlinear
semipositone problem of an $n$th-order delay differential equation.
The main results in this paper generalize some of the existing
results in the literature. The proofs are based on the well-known
Guo-Krasnoselskii fixed-point theorem.

Key words: nonlinear $n$th-order delay differential equations, cone fixed-point theorem, boundary value problems, semipositone problem, positive solutions, nonlinear $n$th-order delay differential equations, cone fixed-point theorem, boundary value problems, semipositone problem