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.

Journal Title

Journal ISSN

Volume Title

Publisher

Mathematical Sciences Publishers.
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.