Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains

Details Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains

2006-04-21

arxiv.org/abs/math/0604469v1

Mathematics

Analysis of PDEs

34 pages, 1 figure

Scientific paper

We study the existence and nonexistence of positive (super) solutions to the nonlinear $p$-Laplace equation $$-\Delta_p u-\frac{\mu}{|x|^p}u^{p-1}=\frac{C}{|x|^{\sigma}}u^q$$ in exterior domains of ${\R}^N$ ($N\ge 2$). Here $p\in(1,+\infty)$ and $\mu\le C_H$, where $C_H$ is the critical Hardy constant. We provide a sharp characterization of the set of $(q,\sigma)\in\R^2$ such that the equation has no positive (super) solutions. The proofs are based on the explicit construction of appropriate barriers and involve the analysis of asymptotic behavior of super-harmonic functions associated to the $p$-Laplace operator with Hardy-type potentials, comparison principles and an improved version of Hardy's inequality in exterior domains. In the context of the $p$-Laplacian we establish the existence and asymptotic behavior of the harmonic functions by means of the generalized Pr\"ufer-Transformation.

Affiliated with

Also associated with

No associations

Rating

Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-627234