Liouville theorems for the weighted Lane–Emden equation with finite Morse indices |
| |
| Authors: | Caisheng Chen Hui Wang |
| |
| Affiliation: | 1. College of Science, Hohai University, Nanjing, China;2. College of Mathematics and Statistics, Yili Normal University, Yining, China |
| |
| Abstract: | In this paper, we study the nonexistence result for the weighted Lane–Emden equation: ![]() (0.1) and the weighted Lane–Emden equation with nonlinear Neumann boundary condition: ![]() (0.2) where f(|x|) and g(|x|) are the radial and continuously differential functions,  is an upper half space in  , and  . Using the method of energy estimation and the Pohozaev identity of solution, we prove the nonexistence of the nontrivial solutions to problems 0.1 and 0.2 under appropriate assumptions on f(|x|) and g(|x|). Copyright © 2017 John Wiley & Sons, Ltd. |
| |
| Keywords: | weighted Lane– Emden equation Liouville theorems Morse index nonexistence |
|
|
is an upper half space in 
, and 
. Using the method of energy estimation and the Pohozaev identity of solution, we prove the nonexistence of the nontrivial solutions to problems 0.1 and 0.2 under appropriate assumptions on f(|x|) and g(|x|). Copyright © 2017 John Wiley & Sons, Ltd.