Nontrivial Solution for a Kirchhoff Type Problem with Zero Mass
Year: 2021
Author: Yanghuan Hu, Haidong Liu, Mingjie Wang, Mengjia Xu
Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 387–395
Abstract
Consider the Kirchhoff type equation −(a+b∫RN|∇u|2dx)Δu=(1|x|μ∗F(u))f(u) in RN, u∈D1,2(RN), (0.1)
where a>0, b≥0, 0<μ<min{N,4} with N≥3, f:R→R is a continuous function and F(u)=∫u0f(t)dt. Under some general assumptions on f, we establish the existence of a nontrivial spherically symmetric solution for problem (0.1). The proof is mainly based on mountain pass approach and a scaling technique introduced by Jeanjean.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v54n4.21.04
Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 387–395
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Kirchhoff type equation zero mass mountain pass approach.
Author Details
Yanghuan Hu Email
Haidong Liu Email
Mingjie Wang Email
Mengjia Xu Email