On some multiple solutions to a p(x)-Laplace equation with supercritical growth

We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle. By means of truncation combined with De Giorgi iteration, we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.