Rellich densities and an application to unconditionally nonoscillatory elliptic equations
John Piepenbrink · Pacific Journal of Mathematics · 1972
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 these equations.