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Volume 31, Issue 3
Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation

Zhu Chaona

DOI: 10.4208/jpde.v31.n3.4

J. Part. Diff. Eq., 31 (2018), pp. 237-251.

Published online: 2018-09

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  • Abstract

In this paper, we consider the following nonlinear elliptic equation △_f^u+hu^α=0 on the complete smooth metric space (Rn, g0, e −f dvg0), where g0 is the Euclidean metric on Rn and f = |x|2/4. We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.

  • Keywords

Gradient estimate Liouville-Type theorem shrinking gradient Ricci soliton.

  • AMS Subject Headings

35J15, 35K10, 58G03, 58G11

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zcn1991@mail.ustc.edu.cn (Zhu Chaona)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-237, author = {Chaona , Zhu}, title = {Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {3}, pages = {237--251}, abstract = {

In this paper, we consider the following nonlinear elliptic equation △_f^u+hu^α=0 on the complete smooth metric space (Rn, g0, e −f dvg0), where g0 is the Euclidean metric on Rn and f = |x|2/4. We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/12707.html} }
TY - JOUR T1 - Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation AU - Chaona , Zhu JO - Journal of Partial Differential Equations VL - 3 SP - 237 EP - 251 PY - 2018 DA - 2018/09 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/12707.html KW - Gradient estimate KW - Liouville-Type theorem KW - shrinking gradient Ricci soliton. AB -

In this paper, we consider the following nonlinear elliptic equation △_f^u+hu^α=0 on the complete smooth metric space (Rn, g0, e −f dvg0), where g0 is the Euclidean metric on Rn and f = |x|2/4. We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.

Chaona , Zhu. (2018). Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation. Journal of Partial Differential Equations. 31 (3). 237-251. doi:10.4208/jpde.v31.n3.4
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