Multiple Solutions of Quasilinear Elliptic Equations in ℝN

الملخص EN

Assume that Q is a positive continuous function in ℝN and satisfies some suitable conditions.

We prove that the quasilinear elliptic equation -Δpu+|u|p-2u=Q(z)|u|q-2u in ℝN admits at least two solutions in ℝN (one is a positive ground-state solution and the other is a sign-changing solution).