Infinitely many solutions for elliptic problems in $\mathbb{R}^N$ involving the $p(x)$-Laplacian - Qing-Mei Zhou; Ke-Qi Wang (Electronic Journal of Qualitative Theory of Differential Equations, 2015)
We consider the $p(x)$-Laplacian equations in $\mathbb{R}^N$. The potential function does not satisfy the coercive condition. We obtain the existence of infinitely many solutions of the equations, improving a recent result of Duan--Huang [L. Duan, L. H. Huang, Electron. J. Qual. Theory Differ. Equ. 2014, No. 28, 1--13].