Nonlocal boundary value problems of arbitrary order

Webb, J.R.L. and Infante, G. (2009) Nonlocal boundary value problems of arbitrary order. Journal of the London Mathematical Society, 79(1), pp. 238-258. (doi: 10.1112/jlms/jdn066)

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We give a new unified method of establishing the existence of multiple positive solutions for a large number of non-linear differential equations of arbitrary order with any allowed number of non-local boundary conditions (BCs). In particular, we are able to determine the Green's function for these problems with very little explicit calculation, which shows that studying a more general version of a problem with appropriate notation can lead to a simplification in approach. We obtain existence and non-existence results, some of which are sharp, and give new results for both non-local and local BCs. We illustrate the theory with a detailed account of a fourth-order problem that models an elastic beam and also determine optimal values of constants that appear in the theory.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Webb, Professor Jeffrey
Authors: Webb, J.R.L., and Infante, G.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of the London Mathematical Society
Journal Abbr.:J. London Math. Soc.
ISSN (Online):1469-7750
Published Online:15 December 2008

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