Positive solutions of nonlocal boundary value problems involving integral conditions

Webb, J.R.L. and Infante, G. (2008) Positive solutions of nonlocal boundary value problems involving integral conditions. No DEA - Nonlinear Differential Equations and Applications, 15(1-2), pp. 45-67. (doi: 10.1007/s00030-007-4067-7)

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Publisher's URL: http://dx.doi.org/10.1007/s00030-007-4067-7


We establish the existence of multiple positive solutions of nonlinear equations of the form -u ''(t) = g(t)f(t, u(t)), t epsilon (0,1) where g, f are non-negative functions, subject to various nonlocal boundary conditions. The common feature is that each can be written as an integral equation, in the space C[0, 1], of the form u(t) = gamma(t)alpha[u] + integral(1)(0) k(t, s)g(s)f(s, u(s))ds where alpha[u] is a linear functional given by a Stieltjes integral but is not assumed to be positive for all positive u. Our new results cover many nonlocal boundary conditions previously studied on a case by case basis for particular positive functionals only, for example, many m-point BVPs are special cases. Even for positive functionals our methods give improvements on previous work. Also we allow weaker assumptions on the nonlinear term than were previously imposed.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Infante, Dr Gennaro and Webb, Professor Jeffrey
Authors: Webb, J.R.L., and Infante, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:No DEA - Nonlinear Differential Equations and Applications
Journal Abbr.:NoDEA
Publisher:Birkhaeuser Verlag AG
ISSN (Online):1420-9004

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