Entire positive solutions of the singular Emden-Fowler equation with nonlinear gradient term

Abstract

Let p and q be locally Hölder functions in R N , p > 0 and q ≥ 0. We study the Emden-Fowler equation, where a 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.