Abstract: The eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is investigated. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, the authors prove the existence of nontrivial solutions for a class of nonlinear elliptic equations with critical potential and indefinite weights in R².

Key words: Eigenvalue problem, Indefinite weights, Critical point theory