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作者机构：Department of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou 450002 China. Department of Mathematical Sciences Georgia Southern University StatesboroGA 30460 USA.
出 版 物：《Journal of Partial Differential Equations》 (偏微分方程（英文版）)
年 卷 期：2013年第26卷第3期
页 面：226-250页
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
主 题：Blow up rate large positive solution quasi-linear elliptic problem uniqueness.
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.
维普期刊数据库