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

Yuan Liang; Qihu Zhang; Chunshan Zhao

doi:10.11650/tjm.18.2014.3327

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

Yuan Liang, Qihu Zhang, Chunshan Zhao

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper we investigate boundary blow-up solutions of the problem where -Δ_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, → 1 as x → ∂Ω). In particular, we do not have the comparison principle.

Original language	American English
Journal	Taiwanese Journal of Mathematics
Volume	18
DOIs	https://doi.org/10.11650/tjm.18.2014.3327
State	Published - Apr 1 2014

Keywords

Boundary blow-up solution
Singularity
Sub-solution
Super-solution
p(x)-Laplacian

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Mathematics

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

abstract = "In this paper we investigate boundary blow-up solutions of the problem where -Δp(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, → 1 as x → ∂Ω). In particular, we do not have the comparison principle.",

keywords = "Boundary blow-up solution, Singularity, Sub-solution, Super-solution, p(x)-Laplacian",

author = "Yuan Liang and Qihu Zhang and Chunshan Zhao",

year = "2014",

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doi = "10.11650/tjm.18.2014.3327",

language = "American English",

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T1 - On the Boundary Blow-Up Solutions of p(x)-Laplacian Equations with Gradient Terms

AU - Liang, Yuan

AU - Zhang, Qihu

AU - Zhao, Chunshan

PY - 2014/4/1

Y1 - 2014/4/1

N2 - In this paper we investigate boundary blow-up solutions of the problem where -Δp(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, → 1 as x → ∂Ω). In particular, we do not have the comparison principle.

AB - In this paper we investigate boundary blow-up solutions of the problem where -Δp(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, → 1 as x → ∂Ω). In particular, we do not have the comparison principle.

KW - Boundary blow-up solution

KW - Singularity

KW - Sub-solution

KW - Super-solution

KW - p(x)-Laplacian

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/324

U2 - 10.11650/tjm.18.2014.3327

DO - 10.11650/tjm.18.2014.3327

M3 - Article

SN - 1027-5487

VL - 18

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

ER -

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

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