Committee Chair

Kong, Lingju

Committee Member

Graef, John R., 1942-; Nichols, Roger; Want, Jin

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

We study the existence of multiple nontrivial solutions for two nonlinear fourth order discrete boundary value problems. We first establish criteria for the existence of at least two nontrivial solutions of the problems and obtain conditions to guarantee that the two solutions are sign-changing. Under some appropriate assumptions, we further prove that the problems have at least three nontrivial solutions, which are respectively positive, negative, and sign-changing. We include two examples to illustrate the applicability of our results. Our theorems are proved by employing variational approaches, combined with the classic mountain pass lemma and a result from the theory of invariant sets of descending flow.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

5-2021

Subject

Calculus of variations; Nonlinear boundary value problems

Keyword

Calculus of variations; DE; Fourth Order; Linear Algebra; PDE

Document Type

Masters theses

DCMI Type

Text

Extent

iv, 36 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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