A Generalization of Ince’s Equation

Ridha Moussa

doi:10.4236/jamp.2014.213137

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Journal of Applied Mathematics and Physi... > Vol.2 No.13, December 2014

A Generalization of Ince’s Equation ()

Ridha Moussa^*

University of Wisconsin, Waukesha, USA.

DOI: 10.4236/jamp.2014.213137 PDF HTML XML 4,018 Downloads 4,557 Views Citations

Abstract

We investigate the Hill differential equation

where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation with one of the above conditions constitutes a regular Sturm-Liouville eigenvalue problem. We investigate the representation of the four Sturm-Liouville operators by infinite banded matrices.

Keywords

Hill Equation, Ince Equation, Sturm-Liouville Problem, Infinite Banded Matrix, Eigenvalues, Eigenfunctions

Share and Cite:

Moussa, R. (2014) A Generalization of Ince’s Equation. Journal of Applied Mathematics and Physics, 2, 1171-1182. doi: 10.4236/jamp.2014.213137.

Conflicts of Interest

The authors declare no conflicts of interest.

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