Eigenvalue problems for quasilinear elliptic systems with limiting nonlinearity |
| |
Authors: | Shen Yaotian Yan Shusen |
| |
Institution: | (1) Department of Applied Mathematics, South China, University of Technology, 510641 Guangzhou, P.R. China;(2) Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 30, 430071 Wuhan, P.R. China |
| |
Abstract: | In this paper, we consider a class of quasilinear elliptic eigenvalue problems with limiting nonlinearity. First, we use the concentration-compactness principle to get the existence of a minimum uεH 0 1 (ω,R N ) of the minimization problem \(I_{\lambda _0 } = \inf \{ \smallint _\Omega (a_{\alpha \beta } (x)g_{ij} (u)D_\alpha u^i D_\beta u^j + h(x)|u|^2 )|u \in H_0^1 (\Omega ,R^N ),\smallint _\Omega |u|^{2n/(n - 2)} = \lambda _0 \} ;\) then we apply the reverse Hölder inequality to prove thatuεL ∞ (ω, R N ). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|