Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions

@article{Eloe2005PositiveSO,
  title={Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions},
  author={Paul W. Eloe and Bashir Ahmad},
  journal={Appl. Math. Lett.},
  year={2005},
  volume={18},
  pages={521-527}
}
We discuss the existence of positive solutions of a nonlinear nth order boundary value problem u(n) + a(t) f (u) = 0, t ∈ (0, 1) u(0) = 0, u′(0) = 0, . . . , u(n−2)(0) = 0, αu(η) = u(1), where 0 < η < 1, 0 < αηn−1 < 1. In particular, we establish the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones due to Krasnoselkiı̌ and Guo. © 2005 Elsevier Ltd. All rights reserved. MSC: 34B15