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 - <p>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&lt;p&lt;\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&lt;p&lt;\infty $, $\lambda $ is a function and $1&lt;\theta</p>