A Generalization of Ince’s Equation

Ridha Moussa^*

University of Wisconsin, Waukesha, USA.

DOI: 10.4236/jamp.2014.213137                

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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