On an open problem involving the p(x)p(x)-Laplacian—A further study on the multiplicity of weak solutions to p(x)p(x)-Laplacian equations

By using a variational method and the truncation technique, we show the multiplicity of weak solutions to a class of p(x)p(x)-Laplacian equations. An open problem proposed by Professor Xianling Fan is solved and more general results are given in this paper.