Positive Solutions of One-Dimensional p-Laplacian Boundary Value Problems for Fourth-Order Differential Equations with Deviating Arguments

T. Jankowski ()
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T. Jankowski: Gdansk University of Technology

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 1, No 3, 47-60

Abstract: Abstract This paper considers the existence of positive solutions of four-point boundary value problems for fourth-order ordinary differential equations with deviating arguments and p-Laplacian. We discuss such problems in the cases when the deviating arguments are delayed or advanced, what may concern optimization issues related to some technical problems. To obtain the existence results, a fixed point theorem for cones due to Avery and Peterson is applied. According to the Author’s knowledge, the results are new. It is a first paper where a fixed point theorem for cones is applied to fourth-order differential equations with deviating arguments and p-Laplacian. An example is included to verify the theoretical results.

Keywords: Fourth-order differential equations; Delayed arguments; Advanced arguments; Positive solutions (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-010-9774-2

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