Existence of three solutions for a class of $(p_1,\ldots,p_n)$-biharmonic systems with Navier boundary conditions
Volume 104 / 2012
Annales Polonici Mathematici 104 (2012), 261-277
MSC: Primary 35G60; Secondary 35B38.
DOI: 10.4064/ap104-3-4
Abstract
We establish the existence of at least three weak solutions for the $(p_{1},\ldots,p_{n})$-biharmonic system $$\begin{cases} {\mit\Delta}(|{\mit\Delta} u_{i}|^{p_i-2}{\mit\Delta} u_{i})=\lambda F_{u_{i}}(x,u_{1},\ldots,u_{n})&\mbox{in }{\mit\Omega},\\ u_{i}={\mit\Delta} u_i=0 &\mbox{on }\partial{\mit\Omega},\end{cases} $$ for $1\leq i\leq n$. The proof is based on a recent three critical points theorem.
