Existence and multiplicity of solutions for nonlocal systems with Kirchhoff type

2014/10/23 by Zhitao Zhang, Zhang, Zhitao, Yimin Sun +1
Mathematics · #35J55 #35J65 #49J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J55 #msc:35J65 #msc:49J40

paper · pdf · doi:10.48550/arxiv.1410.6225

appears in Acta. Math. Applica. Sinica, 2014

arxiv created 2014/10/23 · arxiv updated 2014/10/24

Abstract

Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz. We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.

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