Constant Sign and Sign-Changing Solutions for Quasilinear Elliptic Equations with Neumann Boundary Condition

Through variational methods, sub-supersolution and truncation techniques we prove the existence of three nontrivial solutions for a quasilinear elliptic equation with Neumann boundary condition. We provide sign information for each of these solutions: two of them are of opposite constant sign and the third one is sign changing.