Infinitely Many Clark Type Solutions to a $p(x)$-Laplace Equation

Authors

  • Zheng Zhou School of Applied Mathematical, Xiamen University of Technology, Xiamen, Fujian 361024, P.R.China
  • Xin Si School of Applied Mathematical, Xiamen University of Technology, Xiamen, Fujian 361024, P.R.China

DOI:

https://doi.org/10.4208/jms.v47n4.14.02

Keywords:

Clark theorem, infinitely many solutions, $p(x)$-Laplace, variational methods.

Abstract

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.

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Published

2021-11-08

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Issue

Vol. 47 No. 4 (2014)

Section

Articles

How to Cite

Infinitely Many Clark Type Solutions to a $p(x)$-Laplace Equation. (2021). Journal of Mathematical Study, 47(4), 379-387. https://doi.org/10.4208/jms.v47n4.14.02