Ground State for the Schrödinger Operator with the Weighted Hardy Potential

Abstract EN

We establish the existence of ground states on ℝN for the Laplace operator involving the Hardy-type potential.

This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials.

We also obtain a higher integrability property for the principal eigenfunction.

This is used to examine the behaviour of the principal eigenfunction around 0.