Decay estimation for positive solutions of a $\gamma$-Laplace equation

Abstract

In this paper, we study the properties of the positive solutionsof a $\gamma$-Laplace equation in $R^n$-div$(|\nabla u|^{\gamma-2}\nabla u) =K u^p$,Here $1\gamma$,$p=\frac{(\gamma-1)(n+\gamma)}{n-\gamma}$ and $K(x)$ is a smoothfunction bounded by two positive constants. First, the positivesolution $u$ of the $\gamma$-Laplace equation above satisfies anintegral equation involving a Wolff potential. Based on this, weestimate the decay rate of the positive solutions of the$\gamma$-Laplace equation at infinity. A new method is introducedto fully explore the integrability result established recently byMa, Chen and Li on Wolff type integral equations to derive thedecay estimate.