Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222199 | Nonlinear Analysis: Real World Applications | 2017 | 17 Pages |
Abstract
We consider the following autonomous Kirchhoff-type equation â(a+bâ«RN|âu|2)Îu=f(u),uâH1(RN), where aâ¥0,b>0 are constants and Nâ¥1. Under general Berestycki-Lions type assumptions on the nonlinearity f, we establish the existence results of a ground state and multiple radial solutions for Nâ¥2, and obtain a nontrivial solution and its uniqueness, up to a translation and up to a sign, for N=1. The proofs are mainly based on a rescaling argument, which is specific for the autonomous case, and a new description of the critical values in association with the level sets argument.
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Sheng-Sen Lu,