On $p(x)$-Laplacian equations in ${\mathbb{R}}^N$ with nonlinearity sublinear at zero

Shibo Liu, Chunshan Zhao

Let $p,q$ be functions on ${\mathbb{R}}^N$ satisfying $1\ll q\ll p\ll N$, we consider $p(x)$-Laplacian problems of the form \[ \left\{ \begin{array} [c]{l}% -Δ_{p(x)}u+V(x)\vert u…