... CorporationJournal of Inequalities and ApplicationsVolume 2008, Article ID 612938, 16 pagesdoi:10.1155/2008/612938 Research Article Existence of Solutions for a Class of EllipticSystems inRNInvolving the ... variational methodsis an interesting topic. A lot of researchers have devoted their work to this area 14–22.S. Ogras et al. 13Therefore for px ≥ 2, using 3.30, we have22−pUp|∇un−∇uk|pxdx ... Fr´echet, that is, for fixed u, υ ∈Wpx,qxand given ε>0, there must be a δ ε, u, υ > 0 such that|Fu ω, υ z −Fu, υ −Fu, υω, z|≤εωpx zqx, 3.9 for all ω,...