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### On the generalization of the courant nodal domain theorem

 Citace: DRÁBEK, P., ROBINSON, S. On the generalization of the courant nodal domain theorem. Journal of Differential Equations, 2002, roč. 1, s. 58-71. ISSN: 0022-0396 ČLÁNEK eng On the generalization of the courant nodal domain theorem 2002 Pavel Drábek , Stephen B. Robinson In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if $u_{\lambda_n}$ is an eigenfunction associated with the nth variational eigenvalue, $\lambda_n$, then $u_{\lambda_n}$ has at most 2n -2 nodal domain. Also, if $u_{\lambda_n}$ has n+k nodal domains, then there is another eigenfunction with at most n-k nodal domains.

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