Abstract
In this paper we study the existence of nonnegative supersolutions of the nonlinear elliptic problem −Δu + |∇u|q = λup in the half-space ℝN+, where N = 2, q > 1, p > 0 and λ > 0. We obtain Liouville theorems for positive, bounded supersolutions, depending on the exponents q and p, the dimension N, and, in some critical cases, also on the parameter λ > 0.
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Acknowledgements
J. G.-M. and A. Q. were partially supported by Ministerio de Economía y Competitividad under grants MTM2011-27998 and MTM2014-52822-P (Spain). A. Q. was also partially supported by Fondecyt Grant No. 1151180 Programa Basal, CMM. U. de Chile and Millennium Nucleus Center for Analysis of PDE NC130017.
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García-Melián, J., Quaas, A. & Sirakov, B. Liouville theorems for nonlinear elliptic equations in half-spaces. JAMA 139, 559–583 (2019). https://doi.org/10.1007/s11854-019-0066-y
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DOI: https://doi.org/10.1007/s11854-019-0066-y