Multiple positive solutions for quasilinear elliptic equations of p(x)-Laplacian type with sign-changing nonlinearity

Abstract

We establish sufficient conditions for the existence of multiple positive solutions to nonautonomous quasilinear elliptic equations with p(x)-Laplacian and sign-changing nonlinearity. For solving the Dirichlet boundary-value problem we use variational and topological methods. The nonexistence of positive solutions is also studied.

Keywords

• p(x)-Laplacian
• variable exponent
• sign-changing nonlinearity
• positive solutions
• multiplicity