In this work we will study the eigenvalues for a fourth order elliptic equation with $p(x)$-growth conditions $\Delta^2_{p(x)} u=\lambda |u|^{p(x)-2} u$, under Neumann boundary conditions, where $p(x)$ is a continuous function defined on the bounded domain with $p(x)>1$. Through the Ljusternik-Schnireleman theory on $C^1$-manifold, we prove the existence of infinitely many eigenvalue sequences and $\sup \Lambda =+\infty$, where $\Lambda$ is the set of all eigenvalues.
@article{25626,
title = {Existence of solutions for a fourth order eigenvalue problem ] {Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v34i1.25626},
language = {EN},
url = {http://dml.mathdoc.fr/item/25626}
}
Ben Haddouch, Khalil; El Allali, Zakaria; Tsouli, Najib; El Habib, Siham; Kissi, Fouad. Existence of solutions for a fourth order eigenvalue problem ] {Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i1.25626. http://gdmltest.u-ga.fr/item/25626/