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Synopsis In this paper, we prove various existence and non-existence results for semilinear elliptic problems in unbounded domains. In particular we prove for general classes of unbounded domains that there exists no solution distinct from 0 of for any smooth f satisfying f (0) = 0. This result is obtained by the use of new identities that solutions of semilinear elliptic equations satisfy.
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Esteban et al. (1982) studied this question.
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