PERIODIC AND SEMI-PERIODIC EIGENVALUES OF HILL'S EQUATION WITH SYMMETRIC DOUBLE WELL POTENTIAL

Abstract

In this paper, some estimates are derived explicitly for periodic and semiperiodic eigenvalues of Hill’ s equation with symmetric double well potentials. Also, lengths of the instability intervals are obtained and bounds for the gaps of Dirichlet and Neumann eigenvalues are given by using an auxiliary eigenvalue problem.

Keywords

• Hill’s equation, symmetric double well potential, periodic and semi-periodic eigenvalues, instability intervals.

References

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