On the connection between two quasilinear elliptic problems with source terms of order 0 or 1

Details On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 On the connection between two quasilinear elliptic problems with source terms of order 0 or 1

2008-11-20

arxiv.org/abs/0811.3292v1

Mathematics

Analysis of PDEs

Scientific paper

We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of $\mathbb{R}^{N}.$ The first one, of the form \[ -\Delta_{p}u=\beta(u)| \nabla u| ^{p}+\lambda f(x)+\alpha, \] involves a source gradient term with natural growth, where $\beta$ is nonnegative, $\lambda>0,f(x)\geqq0$, and $\alpha$ is a nonnegative measure. The second one, of the form \[ -\Delta_{p}v=\lambda f(x)(1+g(v))^{p-1}+\mu, \] presents a source term of order $0, $where $g$ is nondecreasing, and $\mu$ is a nonnegative measure. Here $\beta$ and $g$ can present an asymptote. The correlation gives new results of existence, nonexistence, regularity and multiplicity of the solutions for the two problems, without or with measures. New informations on the extremal solutions are given when $g$ is superlinear.

Affiliated with

Also associated with

No associations

Rating

On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 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 On the connection between two quasilinear elliptic problems with source terms of order 0 or 1, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-668520