EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A COUPLED SYSTEM OF KIRCHHOFF TYPE EQUATIONS  

作　　者：Yaghoub JALILIAN 

机构地区：[1]Department of Mathematics,Razi University,Kermanshah,Iran

出　　处：《Acta Mathematica Scientia》2020年第6期1831-1848,共18页数学物理学报（B辑英文版）

摘　　要：In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>1 and 3<α+β<6.We prove the existence of a ground state solution for the above problem in which the nonlinearity is not 4-superlinear at infinity.Also,using a discreetness property of Palais-Smale sequences and the Krasnoselkii genus method,we obtain the existence of infinitely many geometrically distinct solutions in the case whenα,β≥2 and 4≤α+β<6.

关 键 词：Kirchhoff equation Nehari-Pohožave manifold constrained minimization ground state solution 

分 类 号：O175[理学—数学]