Limit-point criteria for symmetric and j-symmetric quasi-differential expressions of even order with a positive definite leading coefficient. (English) Zbl 0614.34011

Frentzen, Hilbert

Fachbereich Mathematik der Universität GHS Essen. 66 p. (1985).

The author presents some limit-point criteria for certain differential expressions with matrix-valued coefficients. The main result gives sufficient conditions for real polynomials in L, where L is a symmetric differential expression of the form \(Ly=W^{-1}\sum^{m}_{i,j=0}(- 1)^ i(Q_{ij}y^{(j)})^{(i)},\) to be limit point up to a fixed degree. On the assumptions of Theorem 3.10, all real polynomials in L are limit-point.
Further theorems are related to differential expressions of the form \[ Ly=W^{-1}\{\sum^{m}_{j=0}(-1)^ j(Q_{2j}y^{(j)})^{(j)}+\sum^{m-1}_{j=0}(-1)^ j[(Q^{\times}_{2j+1}y^{(j+1)})^{(j)}- (Q_{2j+1}y^{(j)})^{(j+1)}]\}, \] where \(Q^{\times}\) denotes the complex conjugate transposed matrix or the transposed matrix of the matrix Q. The results are general and include many of the theorems in the literature.

Reviewer: J.Kalas

MSC:

34A30	Linear ordinary differential equations and systems
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

J-symmetric quasi-differential expressions; limit-point criteria; symmetric differential expression; limit point