| Autor: |
Pavel Drabek, Mitsuharu Otani |
| Jazyk: |
angličtina |
| Rok vydání: |
2001 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Differential Equations, Vol 2001, Iss 48, Pp 1-19 (2001) |
| Druh dokumentu: |
article |
| ISSN: |
1072-6691 |
| Popis: |
We prove that the nonlinear eigenvalue problem for the p-biharmonic operator with $p > 1$, and $Omega$ a bounded domain in $mathbb{R}^N$ with smooth boundary, has principal positive eigenvalue $lambda_1$ which is simple and isolated. The corresponding eigenfunction is positive in $Omega$ and satisfies $frac{partial u}{partial n} < 0$ on $partial Omega$, $Delta u_1 < 0$ in $Omega$. We also prove that $(lambda_1,0)$ is the point of global bifurcation for associated nonhomogeneous problem. In the case $N=1$ we give a description of all eigenvalues and associated eigenfunctions. Every such an eigenvalue is then the point of global bifurcation. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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