Taiwanese Journal of Mathematics
In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions
−div(|∇u| p(x)−2 ∇u) + |u| p(x)−2 u = f(x, u) in Ω,
u = 0 on ∂Ω.
We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-compactness principle, which is of independent interest.
Liang, Yuan, Xianbin Wu, Qihu Zhang, Chunshan Zhao.
"Multiple Solutions of a p(x)-Laplacian Equation Involving Critical Nonlinearities."
Taiwanese Journal of Mathematics, 17 (6): 2083-2100.
doi: 10.11650/tjm.17.2013.3074 source: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/3074