We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first est...We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the SchrSdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2.展开更多
Using transfer function approach, this paper discusses the problem ofsimulaneous stabilization of two SISO plants using a stable controller. It firstgives the equivalence of this problem to the one of simulaneously s...Using transfer function approach, this paper discusses the problem ofsimulaneous stabilization of two SISO plants using a stable controller. It firstgives the equivalence of this problem to the one of simulaneously stabilizingthree SISO plants, and then proposes some necessary and sufficient conditionsfor its solvability.展开更多
基金supported by NSFC(11471331,11101418 and 11271360)
文摘We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the SchrSdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2.
文摘Using transfer function approach, this paper discusses the problem ofsimulaneous stabilization of two SISO plants using a stable controller. It firstgives the equivalence of this problem to the one of simulaneously stabilizingthree SISO plants, and then proposes some necessary and sufficient conditionsfor its solvability.
