**
MATHEMATICA BOHEMICA, Vol. 124, No. 2–3, pp. 273-292 (1999)
**

# Two separation criteria for second order ordinary or partial differential operators

## R. C. Brown, D. B. Hinton

* R. C. Brown*, Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A., e-mail: ` dbrown@gp.as.ua.edu`; * D. B. Hinton*, Department of Mathematics, University of Tennessee, Knoxville, TN 37996, U.S.A., e-mail: ` hinton@novell.math.utk.edu`

**Abstract:**
We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $\Bbb R^n$. Also, for symmetric second-order ordinary differential operators we show that $\limsup_{t\to c} (pq')'/q^2=\theta<2$ where $c$ is a singular point guarantees separation of $-(py')'+qy$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $-\Delta y+qy$ is separated on its minimal domain if $q$ is superharmonic. For $n=1$ the criterion is used to give examples of a separation inequality holding on the domain of the minimal operator in the limit-circle case.

**Keywords:** separation, ordinary or partial differential operator, limit-point, essentially self-adjoint

**Classification (MSC2000):** 34L05, 35P05, 47F05, 34L40, 26D10

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2004—2005 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
for the EMIS Electronic Edition
*