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On singular Sturm–Liouville boundary-value problems

Published online by Cambridge University Press:  04 February 2010

D. D. Hai
Affiliation:
Department of Mathematics, Mississippi State University, Mississippi State, MS 39762, USA

Abstract

We consider the existence of positive solutions for the boundary-value problem

(q(t)ϕ(u′))′ + λf(t,u) = 0, r < t < R,

au(r) − bϕ−1 (q(r))u′(r) = 0, cu(R) + −1(q(R))u′(R) = 0,

where ϕ(u′) = |u′|p−2u′, p > 1, λ > 0, f is p-superlinear or p-sublinear at ∞ and is allowed to become −∞ at u = 0. Our results unify and extend many known results in the literature.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2010

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