Existence and asymptotic behavior of positive ground state solutions for coupled nonlinear fractional Kirchhoff-type systems

Abstract

This paper is concerned with the following linearly coupled fractional Kirchhoff-type system a+b∫R3|(−△)α2u|2dx(−△)αu+λu=f(u)+γv,inR3,c+d∫R3|(−△)α2v|2dx(−△)αv+μv=g(v)+γu,inR3,u,v∈Hα(R3),where a,c,λ,μ>0, b,d≥0 are constants, α∈[34,1) and γ>0 is a coupling parameter. Under the general Berestycki–Lions conditions on the nonlinear terms f and g, we prove the existence of positive vector ground state solutions of Pohožaev type for the above system via variational methods. Moreover, the asymptotic behavior of these solutions as γ→0+ is explored as well. Recent results from the literature are generally improved and extended.