On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds

被引：0
作者：
Alexander Grigor’yan
Yuhua Sun
机构：
[1] Nankai University,School of Mathematical Sciences and LPMC
[2] University of Bielefeld,Department of Mathematics
来源：
Calculus of Variations and Partial Differential Equations | 2019年 / 58卷
关键词：
Primary 58J05; Secondary 35J61;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We determine the critical exponent for certain semi-linear elliptic problem on a Riemannian manifold assuming the volume regularity and Green function estimates.
引用
收藏
相关论文
共 50 条
  • [1] Barlow MT(2004)Which values of the volume growth and escape time exponent are possible for a graph? Rev. Mat. Iberoam. 20 1-31
  • [2] Bidaut-Véron MF(1989)Local and global behavior of solutions of quasilinear equations of Emden–Fowler type Arch. Ration. Mech. Anal. 107 293-324
  • [3] Bidaut-Véron MF(2000)Local behaviour of solutions of a class of nonlinear elliptic systems Adv. Differ. Equ. 5 147-192
  • [4] Caristi G(2008)Liouville theorems for some nonlinear inequalities Proc. Steklov Inst. Math. 260 90-111
  • [5] D’Ambrosio L(2009)Some Liouville theorems for quasilinear elliptic inequalities Dokl. Math. 79 118-124
  • [6] Mitidieri E(1975)Differential equations on Riemannian manifolds and their geometric applications Commun. Pure Appl. Math. 28 333-354
  • [7] Caristi G(1981)Global and local behavior of positive solutions of nonlinear elliptic equations Commun. Pure Appl. Math. 34 525-598
  • [8] Mitidieri E(1999)Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds Bull. Am. Math. Soc. 36 135-249
  • [9] Pohozaev SI(2006)Heat kernels on weighted manifolds and applications Contemp. Math. 398 93-191
  • [10] Cheng SY(2008)Lower estimates for a perturbed Green function J. Anal. Math. 104 25-58
12345