Vol. 12, No. 6, 2019

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Positive solutions to singular second-order boundary value problems for dynamic equations

Curtis Kunkel and Alex Lancaster

Vol. 12 (2019), No. 6, 1069–1080
Abstract

We study singular second-order boundary value problems with mixed boundary conditions on an infinitely discrete time scale. We prove the existence of a positive solution by means of a lower and upper solutions method and the Brouwer fixed-point theorem, in conjunction with perturbation methods used to approximate regular problems.

Keywords
singular boundary value problems, time scales, mixed conditions, lower and upper solutions, Brouwer fixed-point theorem, approximate regular problems
Mathematical Subject Classification 2010
Primary: 34B16, 34B18, 34B40, 39A10
Milestones
Received: 11 February 2019
Revised: 25 March 2019
Accepted: 30 March 2019
Published: 3 August 2019

Communicated by Johnny Henderson
Authors
Curtis Kunkel
Department of Mathematics and Statistics
University of Tennessee at Martin
Martin, TN
United States
Alex Lancaster
Department of Mathematics and Statistics
University of Tennessee at Martin
Martin, TN
United States