Ground state for the Schrödinger operator with the weighted Hardy potential. (English) Zbl 1234.35157
Summary: We establish the existence of ground states on \(\mathbb R^N\) 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.
MSC:
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
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