Local antimaximum principle for the Schrödinger operator in \(\mathbb R^N\). (English) Zbl 1282.35142
Summary: We consider in this paper equations defined in \(\mathbb R^N\) involving Schrödinger operators with indefinite weight functions and with potentials which tend to infinity at infinity. After recalling the existence of principal eigenvalues and the maximum principle, we study the local antimaximum principle.
MSC:
35J10 | Schrödinger operator, Schrödinger equation |
35B50 | Maximum principles in context of PDEs |
35J20 | Variational methods for second-order elliptic equations |
35P15 | Estimates of eigenvalues in context of PDEs |