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Higher order semipositone multi-point boundary value problems on time scales
(PERGAMON-ELSEVIER SCIENCE LTD, 2010) Dogan, Abdulkadir; Graef, John R.; Kong, Lingju
The authors obtain some existence criteria for positive solutions of a higher order semipositone multi-point boundary value problem on a time scale. Applications to some special problems are also discussed. This work extends and complements many results in the literature on this topic. (C) 2010 Elsevier Ltd. All rights reserved.
HIGHER-ORDER SINGULAR MULTI-POINT BOUNDARY-VALUE PROBLEMS ON TIME SCALES
(CAMBRIDGE UNIV PRESS, 2011) Dogan, Abdulkadir; Graef, John R.; Kong, Lingju
We study classes of higher-order singular boundary-value problems on a time scale T with a positive parameter lambda in the differential equations. A homeomorphism and homomorphism phi are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter lambda is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.