We investigate a Hill differential equation with trigonometric polynomial coefficients. we are interested in solutions which are even or odd and have period π or semi-period π. With one of the mentioned boundary conditions, our equation constitute a regular Sturm-Liouville eigenvalue problem. Using Fourier series representation each one of the four Sturm-Liouville operators is represented by an infinite banded matrix. In the particular cases of Ince and Lamé equations, the four infinite banded matrices become tridiagonal. We then investigate the problem of coexistence of periodic solutions and that of existence of polynomial solutions.
|School:||The University of Wisconsin - Milwaukee|
|School Location:||United States -- Wisconsin|
|Source:||DAI-B 76/02(E), Dissertation Abstracts International|
|Keywords:||Hill differential equation, Ince equation, Sturm-Liouville operators|
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