BOUNDEDNESS OF THE NUMBER OF NODAL DOMAINS FOR EIGENFUNCTIONS OF GENERIC

We want to follow the proof of the existence of Delaunay surfaces given in the previous section in order to prove the existence of a smooth family of normal graphs over the

The main results concern the existence and regularity of the minimal partitions and the characterization of the minimal partitions associated with nodal sets as the nodal domains

asymptotic expansion for the first Dirichlet eigenvalue thus showing that the coefficients in this series have a simple explicit expression in terms of the functions defining the

This paper is concerned with analyzing their nodal property of multi-bump type sign-changing solutions constructed by Coti Zelati and Rabinowitz [Comm.. In some cases we provide

The condition f being odd in u allows the authors of [3] to use both positive and negative solutions at the same mountain pass level c as basic one-bump solutions which are glued

Computations are made in the latter case to provide candidates for minimal 3-partitions, using symmetry to reduce the analysis to the determination of the nodal sets of the

For the same implication with Property FM’, it is convenient to first observe that a topological group G has Property FM’ if and only if for every continuous discrete G-set

For finitely generated group that are linear over a field, a polynomial upper bound for these functions is established in [BM], and in the case of higher rank arithmetic groups,