Geodesic
Existence of three solutions for a class of $(p_1,\ldots,p_n)$-biharmonic systems with Navier boundary conditions
Shapour Heidarkhani1 ; Yu Tian2 ; Chun-Lei Tang3
1Department of Mathematics Faculty of Sciences Razi University 67149 Kermanshah, Iran and School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran
2School of Science Beijing University of Posts and Telecommunications Beijing 100876, P.R. China
3School of Mathematics and Statistics Southwest University Chongqing 400715, P.R. China
Annales Polonici Mathematici, Tome 104 (2012) no. 3, pp. 261-277
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap104-3-4
Keywords: establish existence least three weak solutions ldots biharmonic system begin cases mit delta mit delta i mit delta lambda ldots mbox mit omega mit delta mbox partial mit omega end cases leq leq proof based recent three critical points theorem

Shapour Heidarkhani  1   ; Yu Tian  2   ; Chun-Lei Tang  3

1 Department of Mathematics Faculty of Sciences Razi University 67149 Kermanshah, Iran and School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran
2 School of Science Beijing University of Posts and Telecommunications Beijing 100876, P.R. China
3 School of Mathematics and Statistics Southwest University Chongqing 400715, P.R. China 
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     author = {Shapour Heidarkhani and Yu Tian and Chun-Lei Tang},
     title = {Existence of three solutions for a class of
$(p_1,\ldots,p_n)$-biharmonic systems
 with {Navier} boundary conditions},
     journal = {Annales Polonici Mathematici},
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     doi = {10.4064/ap104-3-4},
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Shapour Heidarkhani; Yu Tian; Chun-Lei Tang. Existence of three solutions for a class of
$(p_1,\ldots,p_n)$-biharmonic systems
 with Navier boundary conditions. Annales Polonici Mathematici, Tome 104 (2012) no. 3, pp. 261-277. doi: 10.4064/ap104-3-4

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