Existence of solutions for an elliptic equation with indefinite weight Original Research Article

We consider the elliptic equation with indefinite weight View the MathML source−Δu=V(x)u+f(x,u),u∈H1(RN), Turn MathJax on where V(x)V(x) is a function possibly changing sign in RNRN; under certain assumptions on f(x,u)f(x,u), we obtain the existence of m−nm−n pairs of nontrivial solutions, where m>nm>n, and the mm and nn are all integers.