Infinitely Many Solutions for a Fourth-order Kirchhoff Type Elliptic Problem
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Authors
M. Massar
- Department of Mathematics, University Mohamed I, Oujda, Morocco.
E. M. Hssini
- Department of Mathematics, University Mohamed I, Oujda, Morocco.
N. Tsouli
- Department of Mathematics, University Mohamed I, Oujda, Morocco.
M. Talbi
- CRMEF, Oujda, Morocco.
Abstract
This paper studies the existence of infinitely many solutions for a fourth-order Kirchhoff type elliptic problem\[
\begin{cases}
\Delta\left(|\Delta u |^{p-2}\Delta u\right)-\left[M\left[\int_\Omega |\nabla u |^p dx\right]\right]^{p-1} \Delta_pu+\rho| u|^{p-2}u=\lambda f(x,u),\,\,\,\,\, \texttt{in} \Omega,\\
u=\Delta u=0,\,\,\,\,\, \texttt{on} \partial \Omega.
\end{cases}
\]
Our technical approach is based on Ricceri's principle variational.
Share and Cite
ISRP Style
M. Massar, E. M. Hssini, N. Tsouli, M. Talbi, Infinitely Many Solutions for a Fourth-order Kirchhoff Type Elliptic Problem, Journal of Mathematics and Computer Science, 8 (2014), no. 1, 33 - 51
AMA Style
Massar M., Hssini E. M., Tsouli N., Talbi M., Infinitely Many Solutions for a Fourth-order Kirchhoff Type Elliptic Problem. J Math Comput SCI-JM. (2014); 8(1):33 - 51
Chicago/Turabian Style
Massar, M., Hssini, E. M., Tsouli, N., Talbi, M.. "Infinitely Many Solutions for a Fourth-order Kirchhoff Type Elliptic Problem." Journal of Mathematics and Computer Science, 8, no. 1 (2014): 33 - 51
Keywords
- Navier boundary
- nonlocal
- Ricceri's variational principle.
MSC
- 35J40
- 58E05
- 35D30
- 35J35
- 35J60
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