Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = ...Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = 0. For k ≤ 0, some qualitative properties ofthe solutions are also proved.展开更多
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gord...By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.展开更多
In this paper, we prove the existence of pth moment almost periodic mild solutions in fractional power space to a class of stochastic fractional partial equations using the techniques of contraction fixed point princi...In this paper, we prove the existence of pth moment almost periodic mild solutions in fractional power space to a class of stochastic fractional partial equations using the techniques of contraction fixed point principle, Schauder fixed point theorem and semigroup theorem.展开更多
文摘Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = 0. For k ≤ 0, some qualitative properties ofthe solutions are also proved.
文摘By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
基金partially supported by NSF of Jiangxi Province(Nos.20151BAB212011 and20151BAB201021)NNSF of China(No.11461044)
文摘In this paper, we prove the existence of pth moment almost periodic mild solutions in fractional power space to a class of stochastic fractional partial equations using the techniques of contraction fixed point principle, Schauder fixed point theorem and semigroup theorem.
