Elliptic equations with absorption in a half-space
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We give a necessary and sufficient condition, in the spirit of the classical works by Keller and Osserman, for the elliptic equation Δu = f (u) to have a solution in a half-space of RN. The function f is supposed to be nondecreasing and nonnegative, and we are interested in solutions whose range is where f > 0. The possibility of obtaining such a necessary and sufficient condition has been an open question for a long time.
KeywordsElliptic equations non-existence half-space coercive problems subsolutions
Mathematical subject classification35J60 35J61
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