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Volume 26, Issue 3
Existence, Uniqueness and Blow-up Rate of Large Solutions of Quasi-linear Elliptic Equations with Higher Order and Large Perturbation

Qihu Zhang & Chunshan Zhao

DOI: 10.4208/jpde.v26.n3.3

J. Part. Diff. Eq., 26 (2013), pp. 226-250.

Published online: 2013-09

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  • Abstract

We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem $$-\triangle_{p}u=\lambda (x)u^{\theta -1}-b(x)h(u), in \Omega, $$ with boundary condition $u=+\infty $ on $\partial \Omega $, where $\Omega \subset R^N$ $(N\geq 2)$ is a smooth bounded domain, $1<p<\infty $, $\lambda (.)$ and $b(.)$ are positive weight functions and $h(u)\sim u^{q-1} $ as $u\rightarrow \infty $. Our results extend the previous work [Z. Xie, J. Diff. Equ., 247 (2009), 344-363] from case $p=2$, $\lambda $ is a constant and $\theta =2$ to case $1<p<\infty $, $\lambda $ is a function and $1<\theta

  • Keywords

Blow up rate large positive solution quasi-linear elliptic problem uniqueness

  • AMS Subject Headings

35J25, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhangqh1999@yahoo.com.cn (Qihu Zhang)

czhao@GeorgiaSouthern.edu (Chunshan Zhao)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-26-226, author = {Zhang , Qihu and Zhao , Chunshan}, title = {Existence, Uniqueness and Blow-up Rate of Large Solutions of Quasi-linear Elliptic Equations with Higher Order and Large Perturbation}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {3}, pages = {226--250}, abstract = {

We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem $$-\triangle_{p}u=\lambda (x)u^{\theta -1}-b(x)h(u), in \Omega, $$ with boundary condition $u=+\infty $ on $\partial \Omega $, where $\Omega \subset R^N$ $(N\geq 2)$ is a smooth bounded domain, $1<p<\infty $, $\lambda (.)$ and $b(.)$ are positive weight functions and $h(u)\sim u^{q-1} $ as $u\rightarrow \infty $. Our results extend the previous work [Z. Xie, J. Diff. Equ., 247 (2009), 344-363] from case $p=2$, $\lambda $ is a constant and $\theta =2$ to case $1<p<\infty $, $\lambda $ is a function and $1<\theta

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/5163.html} }
TY - JOUR T1 - Existence, Uniqueness and Blow-up Rate of Large Solutions of Quasi-linear Elliptic Equations with Higher Order and Large Perturbation AU - Zhang , Qihu AU - Zhao , Chunshan JO - Journal of Partial Differential Equations VL - 3 SP - 226 EP - 250 PY - 2013 DA - 2013/09 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/5163.html KW - Blow up rate KW - large positive solution KW - quasi-linear elliptic problem KW - uniqueness AB -

We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem $$-\triangle_{p}u=\lambda (x)u^{\theta -1}-b(x)h(u), in \Omega, $$ with boundary condition $u=+\infty $ on $\partial \Omega $, where $\Omega \subset R^N$ $(N\geq 2)$ is a smooth bounded domain, $1<p<\infty $, $\lambda (.)$ and $b(.)$ are positive weight functions and $h(u)\sim u^{q-1} $ as $u\rightarrow \infty $. Our results extend the previous work [Z. Xie, J. Diff. Equ., 247 (2009), 344-363] from case $p=2$, $\lambda $ is a constant and $\theta =2$ to case $1<p<\infty $, $\lambda $ is a function and $1<\theta

Zhang , Qihu and Zhao , Chunshan. (2013). Existence, Uniqueness and Blow-up Rate of Large Solutions of Quasi-linear Elliptic Equations with Higher Order and Large Perturbation. Journal of Partial Differential Equations. 26 (3). 226-250. doi:10.4208/jpde.v26.n3.3
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