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Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

2014; Wiley; Volume: 38; Issue: 17 Linguagem: Inglês

10.1002/mma.3356

1099-1476

Ravi P. Agarwal, Martin Böhner, А. А. Бойчук, O. P. Strakh,

Differential Equations and Boundary Problems

Mathematical Methods in the Applied SciencesVolume 38, Issue 17 p. 4178-4186 Research Article Fredholm boundary value problems for perturbed systems of dynamic equations on time scales Ravi P. Agarwal, Ravi P. Agarwal Department of Mathematics, Texas A&M University-Kingsville, Kingsville, 78363TXUSASearch for more papers by this authorMartin Bohner, Corresponding Author Martin Bohner Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, 65409–0020, MO, USA Correspondence to: Martin Bohner, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA, E-mail: bohner@mst.eduSearch for more papers by this authorAlexandr Boı̆chuk, Alexandr Boı̆chuk Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, UkraineSearch for more papers by this authorOlexandr Strakh, Olexandr Strakh Taras Shevchenko National University of Kyiv, Kyiv, UkraineSearch for more papers by this author Ravi P. Agarwal, Ravi P. Agarwal Department of Mathematics, Texas A&M University-Kingsville, Kingsville, 78363TXUSASearch for more papers by this authorMartin Bohner, Corresponding Author Martin Bohner Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, 65409–0020, MO, USA Correspondence to: Martin Bohner, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA, E-mail: bohner@mst.eduSearch for more papers by this authorAlexandr Boı̆chuk, Alexandr Boı̆chuk Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, UkraineSearch for more papers by this authorOlexandr Strakh, Olexandr Strakh Taras Shevchenko National University of Kyiv, Kyiv, UkraineSearch for more papers by this author First published: 19 December 2014 https://doi.org/10.1002/mma.3356Citations: 4Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo-inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered. Citing Literature Volume38, Issue1730 November 2015Pages 4178-4186 RelatedInformation