A NOTE ON A LINEAR SPECTRAL THEOREM FOR A CLASS OF FIRST ORDER SYSTEMS IN R-2N

作者：Boscaggin Alberto^*; Garrione Maurizio

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2010, (75): 1-22.

• Spectral theory
• phase angles
• rotation index

Along the lines of Atkinson [3], a spectral theorem is proved for the boundary value problem
{Jz' + f(t)Jz + P(t)z = lambda B(t)z
x(0) = x(T) = 0, t is an element of [0,T], z = (x, y) is an element of R-N x R-N,
where f(t) is real-valued and P(t), B(t) are symmetric matrices, with B(t) positive definite. A suitable rotation index associated to the system is used to highlight the connections between the eigenvalues and the nodal properties of the corresponding eigenfunctions.

• 出版日期2010