Article
On the Boundary Blow-Up Solutions of p(x)-Laplacian Equations with Gradient Terms
Taiwanese Journal of Mathematics
Document Type
Article
Publication Date
4-1-2014
DOI
10.11650/tjm.18.2014.3327
Disciplines
- Education and
- Mathematics
Abstract
In this paper we investigate boundary blow-up solutions of the problem
⎧⎩⎨⎪⎪−△p(x)u+f(x,u)=ρ(x,u)+K(|x|)|∇u|δ(|x|) in Ω, u(x)→+∞ as d(x, ∂Ω)→0,
where −△p(x)u=−div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. The existence of boundary blow-up solutions is proved and the singularity of boundary blow-up solution is also given for several cases including the case of ρ(x,u) being a large perturbation (namely, ρ(x,u(x))f(x,u(x))→1 as x→∂Ω). In particular, we do not have the comparison principle.
Citation Information
Yuan Liang, Qihu Zhang and Chunshan Zhao. "On the Boundary Blow-Up Solutions of p(x)-Laplacian Equations with Gradient Terms" Taiwanese Journal of Mathematics Vol. 18 Iss. 2 (2014) p. 599 - 632 ISSN: 2224-6851 Available at: http://works.bepress.com/chunshan_zhao/19/
This is an open access article retrieved from the Taiwanese Journal of Mathematics.