@Article{JPDE-26-3, 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 = {https://global-sci.com/article/88330/existence-uniqueness-and-blow-up-rate-of-large-solutions-of-quasi-linear-elliptic-equations-with-higher-order-and-large-perturbation} }