On the Solvability of Nonlinear Boundary Value Problems on Time Scales
| dc.contributor.advisor | James Selgrade, Committee Member | en_US |
| dc.contributor.advisor | Ernest Stitzinger, Committee Member | en_US |
| dc.contributor.advisor | Jesus Rodriguez, Committee Chair | en_US |
| dc.contributor.advisor | Kailash Misra, Committee Member | en_US |
| dc.contributor.author | Kalhorn, Rebecca Isabel Burton | en_US |
| dc.date.accessioned | 2010-04-02T19:11:23Z | |
| dc.date.available | 2010-04-02T19:11:23Z | |
| dc.date.issued | 2009-04-27 | en_US |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | dissertation | en_US |
| dc.degree.name | PhD | en_US |
| dc.description | North Carolina State University Theses Mathematics. | |
| dc.description.abstract | In this manuscript we study boundary value problems on time scales. First we will examine weakly nonlinear boundary value problems and analyze problems at resonance; that is, problems where the homogeneous linear boundary value problem has a nontrivial solution space. We establish conditions for the existence of solutions and discuss the dependence of solutions on parameters. Next we consider the existence and properties of solutions to nonlinear dynamic equations of the subject to global boundary conditions. Our most significant result in this section concerns the existence of solutions of problems where the nonlinearity exhibits sublinear growth. Finally we establish sufficient conditions for the solvability of nonlinear scalar two-point boundary value problems at resonance. As a consequence of our results we are able to provide easily verifiable conditions for the existence of periodic behavior for dynamic equations on time scales. | en_US |
| dc.format | Thesis (Ph.D.)--North Carolina State University. | |
| dc.identifier.other | etd-03272009-101325 | en_US |
| dc.identifier.uri | http://www.lib.ncsu.edu/resolver/1840.16/5307 | |
| dc.rights | I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. | en_US |
| dc.subject | Lyapunov Schmidt | en_US |
| dc.subject | Resonance | en_US |
| dc.subject | boundary value problems | en_US |
| dc.subject | time scales | en_US |
| dc.title | On the Solvability of Nonlinear Boundary Value Problems on Time Scales | en_US |
| dcterms.abstract | Keywords: Lyapunov Schmidt, resonance, boundary value problems, time scales. | |
| dcterms.extent | v, 66 pages |
Files
Original bundle
1 - 1 of 1
