Add to ORKGIn this note, we discuss a question posed by T. Hoffmann-Ostenhof (see [3]) concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tori. We present two results. We first show that on the torus (R/2πZ) 2 , a non-constant eigenfunction has an even number of nodal domains. We then consider the torus (R/2πZ) × (R/2ρπZ) , with ρ = 1 √ 3 , and construct on it an eigenfunction with three nodal domains
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
The asymptotic of the number of nodal domains of eigenfunctions on a manifold is closely related to ...
The asymptotic of the number of nodal domains of eigenfunctions on a manifold is closely related to ...
AbstractIn this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear...
International audienceAccording to Courant's theorem, an eigenfunction as\-sociated with the $n$-th ...
International audienceAccording to Courant's theorem, an eigenfunction as\-sociated with the $n$-th ...
We show a partial version of the Courant nodal domain theorem for the p-Laplacian: any eigenfunction...
Generalizing Courant's nodal domain theorem, the ``Extended Courant property'' is the statement that...
We consider a Laplace eigenfunction φλ on a smooth closed Riemannian manifold, that is, satisfying −...
Several types of systems have been put forward during the past few decades to show that there exist ...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
The asymptotic of the number of nodal domains of eigenfunctions on a manifold is closely related to ...
The asymptotic of the number of nodal domains of eigenfunctions on a manifold is closely related to ...
AbstractIn this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear...
International audienceAccording to Courant's theorem, an eigenfunction as\-sociated with the $n$-th ...
International audienceAccording to Courant's theorem, an eigenfunction as\-sociated with the $n$-th ...
We show a partial version of the Courant nodal domain theorem for the p-Laplacian: any eigenfunction...
Generalizing Courant's nodal domain theorem, the ``Extended Courant property'' is the statement that...
We consider a Laplace eigenfunction φλ on a smooth closed Riemannian manifold, that is, satisfying −...
Several types of systems have been put forward during the past few decades to show that there exist ...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
We show that equality in Courant's nodal domain theorem can only be reached for a finite number of e...
The paper addresses the the number of nodal domains for eigenfunctions of Schr\"{o}dinger operators ...