Eigenvalue bounds for Hill's equation

摘要

AbstractFor Hill's equationthe lowest eigenvaluea0of the boundary value problemy(x+ 1) =y(x) is considered. IntroducingLpnorms of the functionf(x), lower bounds fora0which depend only on this norm are derived forp= 1,2 and ∞ by solving a variational principle. For these lower bounds analytical expressions are obtained. The quality of the approximations thus obtained is discussed for Mathieu's equation and an application in magnetohydrodynamics is considere