In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r<sub>1</sub><sub></sub>),...,u((t-r<sub&g...In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r<sub>1</sub><sub></sub>),...,u((t-r<sub>n</sub><sub></sub>)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: H<sup>n</sup><sub>a</sub> → H is a nonlinear mapping, r<sub>1</sub>,...,r<sub>n</sub> are nonnegative constants, and g(t)∈ C(□;H) is bounded. Motivated by [1] [2], we obtain the existence and stability of synchronizing solution under some convergence condition. By this result, we provide a general approach for guaranteeing the existence and stability of periodic, quasiperiodic or almost periodic solution of the equation.展开更多
Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respect...Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the positive solutions of this system. Then using the positive and non-degenerate solution to the scalar equation -△ω ＋ ω = ω3, ω ∈ Hr1（RN）, we construct a synchronized solution branch to prove that for/3 in certain range and fixed, there exist a series of bifurcations in product space R×Hr1（RN）×Hr1（RN） with parameter κ,展开更多
In this paper,the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.
文摘In this paper, we consider an abstract non-autonomous evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r<sub>1</sub><sub></sub>),...,u((t-r<sub>n</sub><sub></sub>)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: H<sup>n</sup><sub>a</sub> → H is a nonlinear mapping, r<sub>1</sub>,...,r<sub>n</sub> are nonnegative constants, and g(t)∈ C(□;H) is bounded. Motivated by [1] [2], we obtain the existence and stability of synchronizing solution under some convergence condition. By this result, we provide a general approach for guaranteeing the existence and stability of periodic, quasiperiodic or almost periodic solution of the equation.
基金supported by National Natural Science Foundation of China(Grant Nos.11325107,11271353 and 11331010)the China Postdoctoral Science Foundation
文摘Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the positive solutions of this system. Then using the positive and non-degenerate solution to the scalar equation -△ω ＋ ω = ω3, ω ∈ Hr1（RN）, we construct a synchronized solution branch to prove that for/3 in certain range and fixed, there exist a series of bifurcations in product space R×Hr1（RN）×Hr1（RN） with parameter κ,
基金Project supported by the National Natural Science Foundation of China(Nos.11831011,11725102).
文摘In this paper,the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.
