Vol. 42, No. 1, 1972

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ISSN: 0030-8730
Rellich densities and an application to unconditionally nonoscillatory elliptic equations

John Piepenbrink

Vol. 42 (1972), No. 1, 195–210
Abstract

Sufficient conditions for embeddings between weighted Sobolev spaces to be compact are derived. These theorems are generalizations of the well known selection principle of Rellich. These results are then applied to the study of the oscillational properties of self-adjoint second order elliptic equations. In addition to reproving some results of Headley and Swanson, new nonoscillation criteria are furnished for lhese equations.

Mathematical Subject Classification 2000
Primary: 46E35
Secondary: 35B05
Milestones
Received: 24 June 1971
Published: 1 July 1972
Authors
John Piepenbrink