Instability intervals of the Ince and Hill equations

摘要

The paper investigates the length L_m of the m-th instability interval of the Hill equation (1+ εA(x))y″+εB(x)y′+(λ+εC(x))y = 0 with A(x), B(x), C(x) being trigonometric polynomials. The leading term in the expansion of L_m in powers of the perturbation parameter ε is found. The results are extensions of earlier work of Levy and Keller (1963).