Geodesic
Existence and concentration of solutions for sublinear fourth-order elliptic equations
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a10/}
}
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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/