Infinitely Many Solutions For A Fourth-order Kirchhoff Type Elliptic Problem
Mohammed Massar, El Miloud Hssini, Najib Tsouli, Mohamed Talbi · Journal of Mathematics and Computer Science · 2014
This paper studies the existence of infinitely many solutions for a fourth-order Kirchhoff type elliptic problem\[ \begin{cases} \Delta\left(|\Delta u |^{p-2}\Delta u\right)-\left[M\left[\int_\Omega | abla u |^p dx\right]\right]^{p-1} \Delta_pu+\rho| u|^{p-2}u=\lambda f(x,u),\,\,\,\,\, \texttt{in} \Omega,\\ u=\Delta u=0,\,\,\,\,\, \texttt{on} \partial \Omega. \end{cases} \] Our technical approach is based on Ricceri's principle variational.