This paper is concerned with the following nonlinear coupled system｛-△u1+ω1u1-1/2△(u21)u1=μ1|u1|p-1u1+β|u2|p+1/2|u1|p-3/2 u1,-△u2+ω2u2-1/2△(u22)u2=μ2|u2|p-1u2+β|u1|p+1/2|u2|μ-3/2 u2,∫Ω|ui|2dx=ρi,i=1,2,(u1,u2)∈ H10(Ω;R2),and linear coupled system｛-△u1+ω1u1-1/2△(u21)u1=μ1|u1|p-1u1+βu2,-△u2+ω2u2-1/2△(u22)u2=μ2|u2|p-1u2+βu1,∫Ω|ui|2dx=ρi,i=1,2,(u1,u2)∈ H10(Ω;R2),where Ω⊂RN(N ≥ 1)is a bounded smooth domain,ωi,β∈R,μi,ρi＞0,i=1,2.Moreover,p＞1 if N=1,2 and 1＜p ≤ 3N+2/N-2 if N≥3.Using change of variables,on the one hand,we prove the existence and stability of normalized solutions in nonlinear coupled system and the limiting behavior of normalized solutions as β →-∞.On the other hand,we apply the minimization constraint technique to obtain the existence of normalized solutions for linear coupled system.Compared with some previous results,we extend the existing results to the quasilinear Schrödinger system and also obtain normalized solutions for the linear coupling case.
关键词
线性与非线性耦合/有界区域/变量替换/正规化解/极限行为
Key words
linear and nonlinear coupled/bounded domains/change of variables/normalized solution/limiting behavior
维普
万方数据