Nonradial Entire Large Solutions of Semilinear Elliptic Equations  

作　　者：LAIR Alan V 

机构地区：[1]Department of Mathematics and Statistics, Air Force Institute of Technology, 2950Hobson Way, Wright Patterson AFB, OH 45433-7765, USA.

出　　处：《Journal of Partial Differential Equations》2010年第4期366-373,共8页偏微分方程（英文版）

摘　　要：We consider the problem of whether the equation △u = p（x）f（u） on RN, N ≥ 3, has a positive solution for which lim ｜x｜→∞（x） = ∞ where f is locally Lipschitz continuous, positive, and nondecreasing on （0,oo） and satisfies ∫1∞[F （t）]^- 1/2dt = ∞ where F（t） = ∫0^tf（s）ds. The nonnegative function p is assumed to be asymptotically radial in a certain sense. We show that a sufficient condition to ensure such a solution u exists is that p satisfies ∫0∞ r min｜x｜=r P （x） dr = ∞. Conversely, we show that a necessary condition for the solution to exist is that p satisfies ∫0∞r1＋ε min ｜x｜=rp（x）dr =∞ for all ε〉0.

关 键 词：Large solution elliptic equation semilinear equation. 

分 类 号：O175.25[理学—数学] O175.8[理学—基础数学]