Eigenvalue Comparisons for Second-Order Linear Equations with Boundary Value Conditions on Time Scales

This paper studies the eigenvalue comparisons for second-order linear equations with boundary conditions on time scales. Using results from matrix algebras, the existence and comparison results concerning eigenvalues are obtained.

[1]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .

[2]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[3]  Milton Philip Olson,et al.  The selfadjoint operators of a von Neumann algebra form a conditionally complete lattice , 1971 .

[4]  C. Travis.  Comparison of eigenvalues for linear differential equations of order $2n$ , 1973 .

[5]  J. Moffat,et al.  On groups of automorphisms of operator algebras , 1977, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  Kato Tosio,et al.  Spectral order and a matrix limit theorem , 1979 .

[7]  A. Peterson,et al.  Comparison theorems for eigenvalue problems for nth order differential equations , 1988 .

[8]  A. Peterson,et al.  A positivity result applied to difference equations , 1989 .

[9]  T. Andô.  Majorization, doubly stochastic matrices, and comparison of eigenvalues , 1989 .

[10]  Darrel Hankerson,et al.  Comparison of eigenvalues for focal point problems for $n$th order difference equations , 1990, Differential and Integral Equations.

[11]  A. Peterson,et al.  Comparison Theorems for a Right Disfocal Eigenvalue Problem , 1994 .

[12]  C. Akemann,et al.  Minimal upper bounds of commuting operators , 1996 .

[13]  John M. Davis,et al.  Comparison of eigenvalues for discrete Lidstone boundary value problems , 1999 .

[14]  R. Agarwal,et al.  Basic Calculus on Time Scales and some of its Applications , 1999 .

[15]  K. R. Prasad,et al.  Comparison of eigenvalues for lidstone boundary value problems on a measure chain (preprint) , 1999 .

[16]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[17]  Jan Hamhalter,et al.  Spectral order of operators and range projections , 2007 .