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

Shapour Heidarkhani; Yu Tian; Chun-Lei Tang

doi:10.4064/ap104-3-4

Geodesic

Parcourir par

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

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

Annales Polonici Mathematici, Tome 104 (2012) no. 3, pp. 261-277.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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

Affiliations des auteurs :

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

@article{10_4064_ap104_3_4,
     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},
     pages = {261--277},
     publisher = {mathdoc},
     volume = {104},
     number = {3},
     year = {2012},
     doi = {10.4064/ap104-3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap104-3-4/}
}

TY  - JOUR
AU  - Shapour Heidarkhani
AU  - Yu Tian
AU  - Chun-Lei Tang
TI  - Existence of three solutions for a class of
$(p_1,\ldots,p_n)$-biharmonic systems
 with Navier boundary conditions
JO  - Annales Polonici Mathematici
PY  - 2012
SP  - 261
EP  - 277
VL  - 104
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap104-3-4/
DO  - 10.4064/ap104-3-4
LA  - en
ID  - 10_4064_ap104_3_4
ER  -

%0 Journal Article
%A Shapour Heidarkhani
%A Yu Tian
%A Chun-Lei Tang
%T Existence of three solutions for a class of
$(p_1,\ldots,p_n)$-biharmonic systems
 with Navier boundary conditions
%J Annales Polonici Mathematici
%D 2012
%P 261-277
%V 104
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap104-3-4/
%R 10.4064/ap104-3-4
%G en
%F 10_4064_ap104_3_4

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. http://geodesic.mathdoc.fr/articles/10.4064/ap104-3-4/

Cité par Sources :