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The existence of positive solutions to a non-local singular boundary value problem

✍ Scribed by Donal O'Regan; Svatoslav Staněk

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
125 KB
Volume
29
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the non‐local singular boundary value problem
where q ∈ C^0^([0,1]) and f, h ∈ C^0^((0,∞)), lim__f__(x)=−∞, lim__h__(x)=∞. We present conditions guaranteeing the existence of a solution x ∈ C^1^([0,1]) ∩ C^2^((0,1]) which is positive on (0,1]. The proof of the existence result is based on regularization and sequential techniques and on a non‐linear alternative of Leray–Schauder type. Copyright © 2005 John Wiley & Sons, Ltd.

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Positive solutions of non-positone Diric
Positive solutions of non-positone Dirichlet boundary value problems with singularities in the phase variables
✍ Ravi P. Agarwal; Donal O'Regan; Svatoslav Staněk 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 181 KB

## Abstract The paper presents existence results for positive solutions of the differential equations __x__ ″ + __μh__ (__x__) = 0 and __x__ ″ + __μf__ (__t, x__) = 0 satisfying the Dirichlet boundary conditions. Here __μ__ is a positive parameter and __h__ and __f__ are singular functions of non‐p