Separation and comparison theorems for classes of singular elliptic inequalities and degenerate elliptic inequalities

Abstract

Separation and comparison theorems of Sturm's type are given for differential inequalities involving singular elliptic operators of the form and a related class of degenerate elliptic operators. The region considered is an open connected subset of the half-space y > 0 in E ^m+l with an open subset of the hyperplane y< = 0 as part of the boundary. A notable feature is that data need not be prescribed on y = 0 in contrast to the regular case where data is prescribed on the entire boundary. The results are obtained by the use of Green's identity and a new Picone-type identity.

^†Present address Michigan State University,E Lansing Michigan.

^†Present address Michigan State University,E Lansing Michigan.

Notes

^†Present address Michigan State University,E Lansing Michigan.