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The optimal shape of a dendrite sealed at both ends

Yannick Privat (2009)

Annales de l'I.H.P. Analyse non linéaire

The $p$ -Laplace eigenvalue problem as $p \to \infty$ in a Finsler metric

M. Belloni, Bernhard Kawohl, P. Juutinen (2006)

Journal of the European Mathematical Society

We consider the $p$ -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite $p$ and investigate the limit problem as $p \to \infty$ .

Upper bound for the number of eigenvalues for nonlinear operators

S. Fučik, J. Nečas, J. Souček, V. Souček (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations

Markus Stammberger, Heinrich Voss (2014)

Applications of Mathematics

Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.