Geodesic
Existence and concentration of solutions for sublinear fourth-order elliptic equations
Electronic journal of differential equations, Tome 2015 (2015)
This article concerns the fourth-order elliptic equations

$\displaylines{ \Delta^{2}u-\Delta u+\lambda V(x)u=f(x, u), \quad x\in \mathbb{R}^N,\cr u\in H^{2}(\mathbb{R}^N), }$

where $\lambda >0$ is a parameter, $V\in C(\mathbb{R}^N)$ and $V^{-1}(0)$ has nonempty interior. Under some mild assumptions, we establish the existence of nontrivial solutions. Moreover, the concentration of solutions is also explored on the set $V^{-1}(0)$ as $\lambda\to\infty$.
Classification : 35J35, 35J60
Keywords: fourth-order elliptic equations, variational method, concentration 
@article{EJDE_2015__2015__a10,
     author = {Zhang,  Wen and Tang,  Xianhua and Zhang,  Jian},
     title = {Existence and concentration of solutions for sublinear fourth-order elliptic equations},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1315.35083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a10/}
}
TY  - JOUR
AU  - Zhang,  Wen
AU  - Tang,  Xianhua
AU  - Zhang,  Jian
TI  - Existence and concentration of solutions for sublinear fourth-order elliptic equations
JO  - Electronic journal of differential equations
PY  - 2015
VL  - 2015
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a10/
LA  - en
ID  - EJDE_2015__2015__a10
ER  - 
%0 Journal Article
%A Zhang,  Wen
%A Tang,  Xianhua
%A Zhang,  Jian
%T Existence and concentration of solutions for sublinear fourth-order elliptic equations
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a10/
%G en
%F EJDE_2015__2015__a10
Zhang,  Wen; Tang,  Xianhua; Zhang,  Jian. Existence and concentration of solutions for sublinear fourth-order elliptic equations. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a10/