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- Title
NODAL SOLUTIONS FOR A CRITICAL KIRCHHOFF TYPE PROBLEM IN R<sup>N</sup>.
- Authors
XIAO-JING ZHONG; CHUN-LEI TANG
- Abstract
In this paper, we consider the existence of nodal solutions of the following Kirchhoff problem (KP)-(a+b∫RN|∇u|2dx)Δu+u=g(u),inRN,where a,b>0 and N≥3. We first prove that (KP) is equivalent to the following system with respect to (u,λ): (Fλ)-Δu+u=g(u),λ-a-bλN-22∫RN|∇u|2dx=0,inRN×R+.For every integer k>0, radial solutions of (KP) with exactly k nodes are obtained by dealing with the system (Fλ) under some suitable assumptions. Moreover, nonexistence results are proved if N≥4 and b is sufficiently large.
- Subjects
KIRCHHOFF'S current law; NODAL analysis; LAPLACIAN matrices; INTEGERS; ELECTRIC currents
- Publication
Topological Methods in Nonlinear Analysis, 2021, Vol 58, Issue 2, p549
- ISSN
1230-3429
- Publication type
Article
- DOI
10.12775/TMNA.2020.076