On the Boundary Blow-Up Solutions of p(x)-Laplacian Equations with Gradient Terms

Authors

• Yuan Liang, Zhejiang Wanli UniversityFollow
• Qihu Zhang, Zhengzhou University of Light Technology
• Chunshan Zhao, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

4-2014

Publication Title

Taiwanese Journal of Mathematics

DOI

10.11650/tjm.18.2014.3327

ISSN

2224-6851

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.

Comments

This is an open access article retrieved from the Taiwanese Journal of Mathematics.

Recommended Citation

Liang, Yuan, Qihu Zhang, Chunshan Zhao. 2014. "On the Boundary Blow-Up Solutions of p(x)-Laplacian Equations with Gradient Terms." Taiwanese Journal of Mathematics, 18 (2): 599-632. doi: 10.11650/tjm.18.2014.3327
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/324

Copyright

This is an open access article retrieved from the Taiwanese Journal of Mathematics.