The Study Of Existence Of Solutions For Two Coupled Choquard Systems

In this thesis,we study two classes of nonlinear coupled Choquard systems with Hardy—Littlewood-Sobolev lower critical exponents by variational methods.First,we consider the following coupled Choquard systems with magnetic fields#12 where N≥3,α∈(0,N),Iα:RN\{0}→R is a Riesz potential of order,the magnetic potential A(x)∈C(RN,RN),V(x)is the progressive periodic potential,the function f satisfies suitable subcritical growth condition,F(s)=∫0s f(t)dt.We apply Nehari manifold method and concentration compactness principle to prove the existence of ground states of this system.Next,we consider the following coupled Choquard systems with variable potentials and nonlinear perturbation terms#12 where N≥3,λ>0,α∈(0,N),Iα:RN\{0}→R is a Riesz potential of order,N+α/N<p<N+α/N-2,V is a non-negative continuous and variable potential.By using the Pohozaev manifold,we prove that there exists a constant λ*>0 such that the system has a ground state solution if λ>λ*.