Geodesic
Continuous spectrum of a fourth order nonhomogeneous elliptic equation with variable exponent
Electronic Journal of Differential Equations, Tome 2011 (2011).

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

Summary: In this article, we consider the nonlinear eigenvalue problem $$\displaylines{ \Delta(|\Delta u|^{p(x)-2}\Delta u )=\lambda |u|^{q(x)-2}u\quad \hbox{in }\Omega, \cr u=\Delta u = 0\quad \hbox{on }\partial\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ with smooth boundary and $ p, q: \overline{\Omega} \to (1,+\infty)$ are continuous functions. Considering different situations concerning the growth rates involved in the above quoted problem, we prove the existence of a continuous family of eigenvalues. The proofs of the main results are based on the mountain pass lemma and Ekeland's variational principle.
Classification : 35G30, 35K61, 46E35
Keywords: fourth order elliptic equation, eigenvalue, Navier condition, variable exponent, Sobolev space, mountain pass theorem, Ekeland's variational principle 
@article{EJDE_2011__2011__a11,
     author = {Ayoujil, Abdesslem and El Amrouss, Abdel Rachid},
     title = {Continuous spectrum of a fourth order nonhomogeneous elliptic equation with variable exponent},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a11/}
}
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Ayoujil, Abdesslem; El Amrouss, Abdel Rachid. Continuous spectrum of a fourth order nonhomogeneous elliptic equation with variable exponent. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a11/