Least energy nodal solution for Kirchhoff type problem with an asymptotically 4-linear nonlinearity

Least energy nodal solution for Kirchhoff type problem with an asymptotically 4-linear nonlinearity

In the present paper, we consider the following Kirchhoff type problem −(a+b∫R3|∇u|2dx)Δu+V(x)u=f(u)inR3,where a,b>0 and the potential V has double potential well. With an asymptotically 4-linear nonlinearity f, we prove that the Kirchhoff type problem has one least energy nodal solution by varia...

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Veröffentlicht in:Applied mathematics letters 2020-04, Vol.102, p.106157, Article 106157
1. Verfasser: Xie, Qilin
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotically 4-linear
Kirchhoff type problem
Mathematics
Mathematics, Applied
Nodal solution
Physical Sciences
Science & Technology
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Zusammenfassung:In the present paper, we consider the following Kirchhoff type problem −(a+b∫R3|∇u|2dx)Δu+V(x)u=f(u)inR3,where a,b>0 and the potential V has double potential well. With an asymptotically 4-linear nonlinearity f, we prove that the Kirchhoff type problem has one least energy nodal solution by variational methods.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2019.106157