Semipositone m-point boundary-value problems

Date

2004-10-10

Authors

Kosmatov, Nickolai

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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. Electronic Journal of Differential Equations, 2004(119), pp. 1-7.

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Attribution 4.0 International

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