Existence of radial solutions for a p(x) -Laplacian Dirichlet problem

In this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized p(x) -Laplacian problem − Δ p(x)u+ R(x) up(x)−2u= a(x) | u| q(x)−2u− b(x) | u| r(x)−2u with Dirichlet boundary condition in the unit ball in RN (for N≥ 3), where a, b, R are radial functions. © 2021, The Author(s).