Infinitely Many Clark Type Solutions to a $p(x)$-Laplace Equation (Journal of Mathematical Study, 2021)
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 infinitelymany solutions as well as the structure of the set of critical points near the origin areobtained.