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

Kunkel, Curtis; Lancaster, Alex

doi:10.2140/involve.2019.12.1069

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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

DOI: 10.2140/involve.2019.12.1069

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

Vol. 12, No. 6, 2019