Boundary data smoothness for solutions of nonlocal boundary value problems.
Date
2011-05
Authors
Lyons, Jeffrey W.
Access rights
Worldwide access.
Access changed 6/26/13.
Access changed 6/26/13.
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematical Sciences Publishers.
International Publications.
Academic Publications.
International Publications.
Academic Publications.
Abstract
In this dissertation, we investigate boundary data smoothness for solutions of nonlocal boundary value problems over discrete and continuous domains. Essentially, we show that under certain conditions partial derivatives and differences exist, with respect to boundary conditions, for solutions of nonlocal boundary value problems and solve the variational equation in the derivative case and a specific linear difference equation in the difference case. Lastly, we provide a corollary and a few examples as well as some ideas for future work.
Description
Keywords
Ordinary differential equations., Difference equations., Nonlocal boundary value problem.
Citation
Henderson, J., Hopkins, B., Kim. E., and Lyons,J. "Boundary data smoothness for solutions of nonlocal boundary value problems for nth order differential equations." Involve: A Journal of Mathematics 1 no. 2 (2008): 167-181.
Hopkins, B., Kim, E., Lyons, J., and Speer, K. "Boundary data smoothness for solutions of nonlocal boundary value problems for second order difference equations." Communications on Applied Nonlinear Analysis 2 no. 2 (2009): 1-12.
Henderson, J., Lyons, J. "Characterization of partial derivatives with respect to boundary conditions for solutions of nonlocal boundary value problems for nth order differential equations." International Journal of Pure and Applied Mathematics 56 (2009): 235-257.
Hopkins, B., Kim, E., Lyons, J., and Speer, K. "Boundary data smoothness for solutions of nonlocal boundary value problems for second order difference equations." Communications on Applied Nonlinear Analysis 2 no. 2 (2009): 1-12.
Henderson, J., Lyons, J. "Characterization of partial derivatives with respect to boundary conditions for solutions of nonlocal boundary value problems for nth order differential equations." International Journal of Pure and Applied Mathematics 56 (2009): 235-257.