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We are concerned with the existence of rapidly decaying solutions for the equationK (x) := exp(|x| α /4), α 2 and the number β is given by β := (α − 2) (2 * −q) (2 * −2) . We obtain a positive solution if 2 < q < 2 * and a sign changing solution if q = 2. The existence results depend on the values of the parameter λ. In the proofs we apply variational methods.

In this paper we are concerned with the number of nonnegative solutions of the elliptic system (P )

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