Existence of three solutions for a class of $(p_1,\ldots,p_n)$-biharmonic systems with Navier boundary conditions

Volume 104 / 2012

Shapour Heidarkhani, Yu Tian, Chun-Lei Tang Annales Polonici Mathematici 104 (2012), 261-277 MSC: Primary 35G60; Secondary 35B38. DOI: 10.4064/ap104-3-4


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.


  • Shapour HeidarkhaniDepartment of Mathematics
    Faculty of Sciences
    Razi University
    67149 Kermanshah, Iran
    School of Mathematics
    Institute for Research in Fundamental Sciences (IPM)
    P.O. Box 19395-5746, Tehran, Iran
  • Yu TianSchool of Science
    Beijing University of Posts and Telecommunications
    Beijing 100876, P.R. China
  • Chun-Lei TangSchool of Mathematics and Statistics
    Southwest University
    Chongqing 400715, P.R. China

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