Extremal values of eigenvalues of Sturm–Liouville operators with potentials in balls (original) (raw)

This paper is a continuation of Zhang [M. Zhang, Continuity in weak topology: Higher order linear systems of ODE, Sci. China Ser. A 51 (2008) 1036-1058; M. Zhang, Extremal values of smallest eigenvalues of Hill's operators with potentials in L 1 balls, J. Differential Equations 246 (2009) 4188-4220]. Given a potential q ∈ L p ([0, 1], R), p ∈ [1, ∞]. We use λ m (q) to denote the mth Dirichlet eigenvalue of the Sturm-Liouville operator with potential q(t), where m ∈ N. The minimal value L m,p (r) and the maximal value M m,p (r) of λ m (q) with potentials q in the L p ball of radius