Geodesic
Global bifurcation result for the $p$-biharmonic operator
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove that the nonlinear eigenvalue problem for the p-biharmonic operator with $p greater than 1$, 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 $\partial \Omega, \Delta u_1 less than 0$ 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.
Classification : 35P30, 34C23
Keywords: p-biharmonic operator, principal eigenvalue, global bifurcation 
@article{EJDE_2001__2001__a138,
     author = {Dr\'abek, Pavel and \^Otani, Mitsuharu},
     title = {Global bifurcation result for the $p$-biharmonic operator},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a138/}
}
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Drábek, Pavel; Ôtani, Mitsuharu. Global bifurcation result for the $p$-biharmonic operator. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a138/