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Green's functions and eigenvalue comparisons for higher order dynamic equations on time scales
The Introduction briefly discusses calculus on time scales, initially developed by Stefan Hilger in 1988. For functions f : T→R 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. ^
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.