A Brezis-Nirenberg type theorem on local minimizers for p(x)-Kirchhoff Dirichlet problems and applications
Xianling Fan · Differential Equations & Applications · 2010
This paper deals with a class of p(x) -Kirchhoff Dirichlet problems possessing a variational structure which corresponds to the variational functional E defined on W 1,p(x) 0 () . We prove a Brezis-Nirenberg type theorem which asserts that every local minimizer of E in the C 1 () topology is also a local minimizer of E in the W 1,p(x) 0