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

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 = {Qihu and Zhang and zhangqh1999@yahoo.com.cn and 4452 and Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China and Qihu Zhang and Chunshan and Zhao and czhao@GeorgiaSouthern.edu and 12120 and Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA and Chunshan Zhao}, 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

Qihu Zhang & Chunshan Zhao. (2019). 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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