TY - JOUR T1 - Infinitely Many Clark Type Solutions to a $p(x)$-Laplace Equation AU - Zhou , Zheng AU - Si , Xin JO - Journal of Mathematical Study VL - 4 SP - 379 EP - 387 PY - 2014 DA - 2014/12 SN - 47 DO - http://doi.org/10.4208/jms.v47n4.14.02 UR - https://global-sci.org/intro/article_detail/jms/9963.html KW - Clark theorem, infinitely many solutions, $p(x)$-Laplace, variational methods. AB -

In this paper, the following $p(x)$-Laplacian equation: $$Δ_{p(x)}u+V(x)|u|^{p(x)-2}u=Q(x)f(x,u), \ \ x∈\mathbb{R}^N,$$ is studied. By applying an extension of Clark's theorem, the existence of infinitely many solutions as well as the structure of the set of critical points near the origin are obtained.