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We consider a semilinear elliptic equation with an indefinite unbounded potential and a Carathéodory reaction term that exhibits superlinear growth near ±∞ without satisfying the AR-condition. Also, at the origin, the primitive of the reaction satisfies a nonuniform nonresonance condition with respect to the first eigenvalue of {Mathematical expression} . Using critical point theory and Morse theory, we show that the problem has at least three nontrivial smooth solutions. Our result extends that of Wang (Anal Nonlineaire 8:43-58, 1991). © 2011 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag

Multiple solutions for superlinear Dirichlet problems with an indefinite potential