Multiplicity of positive and nodal solutions for an inhomogeneous nonlinear elliptic problem

In this paper, we show that there exist λ>2λ>2 and C>0C>0 such that a(x)−1≥−Ce−λ|x|for all x∈RN, the nonlinear elliptic problem −Δu+u=a(x)|u|p−2u+f(x)−Δu+u=a(x)|u|p−2u+f(x) in RNRN has a solution that changes sign in RNRN, in addition to two positive solutions.