Positive solutions of the p(x)p(x)-Laplace equation with singular nonlinearity

In this paper, using sub–supersolution method, we study the positive solution of the p(x)p(x)-Laplacian equations −Δp(x)u=f(x,u)−Δp(x)u=f(x,u) with Dirichlet boundary condition on a bounded domain ΩΩ in RnRn with C1,ω¯ boundary for some 0<ω¯<1 for a possibly singular nonlinearity ff on Ω×(0,∞)Ω×(0,∞).