- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:42
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
3
1987
3
Eigenvalue Problems of Quasilinear Elliptic Systems on $R^n$
Gongbao
Li
Huazhong Normal University, WUHAN, CHINA
In this paper, we get the existence results of the nontrivial weak solution $(\lambda, u)$ of the following eigenvalue problem of quasilinear elliptic systems $$–D_\alpha (a_{\alpha \beta}(x, u)D_\beta u^i) + \frac{1}{2}D_{u^i}a_{\alpha \beta}(x, u)D_\alpha u^jD_\beta u^j + h(x)u^i = \lambda |u|^{p–2}u^i,$$ for $x \in \mathbb R^n$, $1 ≤ i ≤ N$ and $$u = (u^1, u^2, ..., u^N) \in E = \{ \nu = (\nu^1, \nu^2, ..., \nu^N) | \nu^i \in H^1 (\mathbb R^n), 1 ≤ i ≤ N \},$$ where $a_{\alpha \beta} (x, u)$ satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before.
General
371
399
10.4171/RMI/55
http://www.ems-ph.org/doi/10.4171/RMI/55