Abstract
Let p and q be locally Hölder functions in ℝN, p > 0 and q ≥ 0. We study the Emden-Fowler equation \(-\triangle u+q(x)\mid \nabla u\mid^\alpha=p(x)u^{-\gamma}\) in ℝN, where α and γ are positive numbers. Our main result establishes that the above equation has a unique positive solutions decaying to zero at infinity. Our proof is elementary and it combines the maximum principle for elliptic equations with a theorem of Crandall, Rabinowitz and Tartar.
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Dinu, TL. Entire positive solutions of the singular Emden-Fowler equation with nonlinear gradient term. Results. Math. 43, 96–100 (2003). https://doi.org/10.1007/BF03322725
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DOI: https://doi.org/10.1007/BF03322725