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Zeitschrift für Analysis und ihre Anwendungen


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Volume 29, Issue 4, 2010, pp. 469–485
DOI: 10.4171/ZAA/1419

Published online: 2010-10-02

A Quasilinear Eigenvalue Problem with Robin Conditions on the Non-Smooth Domain of Finite Measure

Pavel Drábek[1] and S. H. Rasouli[2]

(1) University of West Bohemia, Plzen, Czech Republic
(2) Babol University of Technology, Iran

In this paper, we consider a nonlinear eigenvalue problem involving the p-Laplacian with Robin boundary conditions on a domain of finite measure. We show the existence, simplicity and isolation of principal eigenvalue and regularity results for the corresponding eigenfunction. Furthermore we establish the link between the Dirichlet and Neumann problems by means of the Robin boundary conditions with variable parameter.

Keywords: Nonlinear eigenvalue problem, p-Laplacian, Robin boundary conditions, Non-smooth domains

Drábek Pavel, Rasouli S.: A Quasilinear Eigenvalue Problem with Robin Conditions on the Non-Smooth Domain of Finite Measure. Z. Anal. Anwend. 29 (2010), 469-485. doi: 10.4171/ZAA/1419