Ordinary Differential Equations and Applied Dynamics Commons^™

Isospectral Sets For Fourth-Order Ordinary Differential Operators, Lester Caudill, Peter A. Perry, Albert W. Schueller

Department of Math & Statistics Faculty Publications

Let L(p)u = D⁴u - (p₁u’)’ + p₂u be a fourth-order differential operator acting on L²[0; 1] with p ≡ (p1; p2) belonging to L²_ℝ[0, 1] x L²_ℝ[0, 1] and boundary conditions u(0) = u''(0) = u(1) = u''(1) = 0. We study the isospectral set of L(p) when L(p) has simple spectrum. In particular we show that for such p …