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Positive solutions of a second-order boundary value problem via integro-differential equation arguments

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Abstract:

The objective of this article is to establish the existence and multiplicity of positive solutions for the second-order boundary value problem depending on the first-order derivative u':  [image omitted] Our way to overcome the difficulty resulting from the first-order derivative is to transform it into an initial problem of a first-order integro-ordinary differential equation. Then, based on a priori estimates of positive solutions of an auxiliary problem, we use index theory to establish the existence and multiplicity of positive solutions for the above problem. The main results are used to establish the existence of symmetric positive solutions for the Dirichlet problem.

Keywords: Dirichlet problem; integro-ordinary differential equation; positive solution; symmetric positive solution

Document Type: Research Article

DOI: https://doi.org/10.1080/00036810903157212

Affiliations: 1: Department of Mathematics, Qingdao Technological University, Qingdao, PR China 2: Department of Mathematics, National University of Ireland, Galway, Ireland 3: Department of Mathematical Science, Florida Institute of Technology, Melbourne, FL 32901, USA

Publication date: 2009-08-01

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