Existence of positive solutions for a thermostat model

Webb, J.R.L. (2012) Existence of positive solutions for a thermostat model. Nonlinear Analysis: Real World Applications, 13(2), pp. 923-938. (doi: 10.1016/j.nonrwa.2011.08.027)

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We study a second order nonlinear boundary value problem subject to some nonlocal boundary conditions, which models a thermostat. The sensors are linear functionals, one gives feedback from part of the interval to a controller at one endpoint, the other gives feedback to a controller at the other endpoint. We determine the Green's function and establish its useful properties which enables us to establish the existence of multiple positive solutions and to prove nonexistence results. We calculate all relevant constants in some explicit examples.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Webb, Professor Jeffrey
Authors: Webb, J.R.L.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Nonlinear Analysis: Real World Applications
ISSN (Online):1878-5719
Published Online:29 September 2011

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