摘要：In this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized $p(x)$ -Laplacian problem $$ -\Delta _{p(x)} u R(x) u^{p(x)-2}u=a (x) \vert u \vert ^{q(x)-2} u- b(x) \vert u \vert ^{r(x)-2} u $$ with Dirichlet boundary condition in the unit ball in $\mathbb{R}^{N}$ (for $N \geq 3$ ), where a, b, R are radial functions.
