Existence of multiple solutions for weighted p(r)p(r)-Laplacian equation Dirichlet problems

This paper deals with the existence of multiple solutions for weighted p(r)p(r)-Laplacian equation Dirichlet problems. Several sub-super-solution type results have been given via Leray–Schauder’s degree method. In particular, we give a counterexample which means that Ωα2Ωα2 in paper [J. Henderson, H.B. Thompson, Existence of multiple solutions for second order boundary value problems, J. Differential Equations 166 (2000) 443–454] is not an open subset of C01.