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

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

Year:    2013

Author:    Qihu Zhang, Chunshan Zhao

Journal of Partial Differential Equations, Vol. 26 (2013), Iss. 3 : pp. 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

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v26.n3.3

Journal of Partial Differential Equations, Vol. 26 (2013), Iss. 3 : pp. 226–250

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Blow up rate

Author Details

Qihu Zhang

Chunshan Zhao

  1. Metasolutions of Parabolic Equations in Population Dynamics

    Bibliography

    2015

    https://doi.org/10.1201/b19418-15 [Citations: 0]