Positive solutions of a nonlinear higher order boundary-value problem
Date
2007-03-15
Authors
Graef, John
Henderson, Johnny
Yang, Bo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
The authors consider the higher order boundary-value problem
u(n)(t) = q(t)ƒ(u(t)), 0 ≤ t ≤ 1,
u(i-1)(0) = u(n-2)(p) = u(n-1)(1) = 0, 1 ≤ i ≤ n - 2,
where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.
Description
Keywords
Existence and nonexistence of positive solutions, Guo-Krasnosel'skii fixed point theorem, Higher order boundary value problem
Citation
Graef, J. R., Henderson, J., & Yang, B. (2007). Positive solutions of a nonlinear higher order boundary-value problem. <i>Electronic Journal of Differential Equations, 2007</i>(45), pp. 1-10.
Rights
Attribution 4.0 International