Graef, John R., 1942-; Nichols, Roger; Want, Jin
College of Arts and Sciences
University of Tennessee at Chattanooga
Place of Publication
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.
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.
Calculus of variations; Nonlinear boundary value problems
iv, 36 leaves
Layne, Danielle, "Nontrivial solutions for nonlinear discrete boundary value problems of the fourth order" (2021). Masters Theses and Doctoral Dissertations.