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

作　　者：ZHANG Qihu ZHAO Chunshan 

机构地区：[1]Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China. [2]Department of Mathematical Sciences, Georgia Southern University, Statesboro,GA 30460, USA.

出　　处：《Journal of Partial Differential Equations》2013年第3期226-250,共25页偏微分方程（英文版）

基　　金：Acknowledgments Research is partly supported by the National Science Foundation of China （10701066 ＆ 10971087）.

摘　　要：We establish the existence, uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem -△pu=λ（x）u^θ-1-b（x）h（u）, in Ω,with boundary condition u = ＋∞ on δΩ, where Ω R^N （N≥2） is a smooth bounded domain, 1 〈 p 〈∞ λ（·） and b（·） are positive weight functions and h（u） ～ uq-1 as u → ∞. Our results extend the previous work [Z. Xie, J. Diff. Equ., 247 （2009）, 344-363] from case p = 2, λ is a constant and θ = 2 to case 1 〈 p 〈∞, A is a function and 1 （ 0 〈 θ 〈q 〉 p）; and also extends the previous work [Z. Xie, C. Zhao, J. Diff. Equ., 252 （2012）, 1776-1788], from case A is a constant and θ = p to case λ is a function and 1 〈 θ 〈 q （ 〉 p）. Moreover, we remove the assumption of radial symmetry of the problem and we do not require h（·） is increasing.

关 键 词：Blow up rate large positive solution quasi-linear elliptic problem uniqueness. 

分 类 号：O175.25[理学—数学]