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We show that for a class of semilinear elliptic equations there are at least three nontrivial solutions. Existence of infinitely many solutions is also shown when the nonlinear term is odd. In our results, the nonlinear term can grow super-critically at infinity.doi:10.1090/s0002-9939-97-04199-3 fatcat:psz4trdwmzfrdb4pxkgsjqgjqq