On the positive solutions to some quasilinear elliptic partial differential equations

arXiv0904.1489MaRDI QIDQ6213481

Octavian Mustafa, Yong Zhou

Publication date: 9 April 2009

Abstract: We establish that the elliptic equation $Deltau+f(x,u)+g(|x|)xcdotablau=0$, where $xinmathbb{R}^n$, $ngeq3$, and $|x|>R>0$, has a positive solution which decays to 0 as $|x|o+infty$ under mild restrictions on the functions $f,g$. The main theorem extends and complements the conclusions of the recent paper [M. Ehrnstr"{o}m, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), 1147--1154]. Its proof relies on a general result about the long-time behavior of the logarithmic derivatives of solutions for a class of nonlinear ordinary differential equations and on the comparison method.

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Theoretical approximation in context of PDEs (35A35)

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