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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- P. Pucci and J. Serrin. The maximum principle. Progress in Nonlinear Differential Equations and their Applications, 73. Birkhauser Verlag, Basel (2007).Google Scholar
- V. Rădulescu. Singular phenomena in nonlinear elliptic problems: from boundary blow-up solutions to equations with singular nonlinearities, in “Handbook of Differential Equations: Stationary Partial Differential Equations”, Vol. 4 (Michel Chipot, Editor) (2007), 483–591.Google Scholar