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Green's functions and eigenvalue comparisons for higher order dynamic equations on time scales
Abstract
The Introduction briefly discusses calculus on time scales, initially developed by Stefan Hilger in 1988. For functions f : [special characters omitted] we introduce the delta derivative with the corresponding integral and state fundamental results. In Chapter 2 the existence of the Green's function is shown for both conjugate and focal boundary value problems. In some cases, a form for the Green's function which relies on recursive function definitions is found, making calculations for specific examples significantly simpler. In Chapter 3, the form of the Green's function from Chapter 2 is used to find the sign of the Green's function for a focal boundary value problem. These sign conditions along with traditional cone theory are then used to do eigenvalue comparisons for more complicated dynamic equations. In Chapter 4, we examine a basic partial differential equation on time scales, and when there exists a positive traveling wave solution.
Subject Area
Mathematics
Recommended Citation
Hoffacker, Joan, "Green's functions and eigenvalue comparisons for higher order dynamic equations on time scales" (2001). ETD collection for University of Nebraska-Lincoln. AAI3009725.
https://digitalcommons.unl.edu/dissertations/AAI3009725