Semipositone m-point boundary-value problems
Date
2004-10-10
Authors
Kosmatov, Nickolai
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We study the m-point nonlinear boundary-value problem
-[p(t)u' (t)]' = λƒ (t, u(t)), 0 < t < 1,
u'(0) = 0, ∑m-2i=1 αiu(ηi) = u(1),
where 0 < η1 < η2 < ··· < ηm-2 < 1, αi > 0 for 1 ≤ i ≤ m - 2 and ∑m-2i=1 αi < 1, m ≥ 3. We assume that p(t) is non-increasing continuously differentiable on (0, 1) and p(t) > 0 on [0, 1]. Using a cone-theoretic approach we provide sufficient conditions on continuous ƒ(t, u) under which the problem admits a positive solution.
Description
Keywords
Green's function, Fixed point theorem, Positive solutions, Multi-point boundary-value problem
Citation
Kosmatov, N. (2004). Semipositone m-point boundary-value problems. <i>Electronic Journal of Differential Equations, 2004</i>(119), pp. 1-7.
Rights
Attribution 4.0 International