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 - <p style="text-align: justify;">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&#39;s theorem, the existence of infinitely
many solutions as well as the structure of the set of critical points near the origin are
obtained.</p>