In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases. Periodic equilibrium solutions are found anal...In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter k through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics.展开更多
Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients ar...Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.展开更多
Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point o...Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f);3) For any z ε R(f), the set w (z,f) is finite;4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].展开更多
Let T be a tree and f be a continuous map from T into itself. We show mainly in this paper that a point x of T is an w-limit point of f if and only if every open neighborhood of x in T contains at least nx + 1 points ...Let T be a tree and f be a continuous map from T into itself. We show mainly in this paper that a point x of T is an w-limit point of f if and only if every open neighborhood of x in T contains at least nx + 1 points of some trajectory, where nx equals the number of connected components of T \ {x}. Then, for any open subset G w(f) in T, there exists a positive integer m = m(G) such that at most m points of any trajectory lie outside G.This result is a generalization of the related result for maps of the interval.展开更多
文摘In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter k through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics.
基金The Natural Science Foundation of Hunan Province !(No .97JJN 70 )
文摘Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.
文摘Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f);3) For any z ε R(f), the set w (z,f) is finite;4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].
基金The NSFC(19961001) and the NSF(9811022) of Guangxi.
文摘Let T be a tree and f be a continuous map from T into itself. We show mainly in this paper that a point x of T is an w-limit point of f if and only if every open neighborhood of x in T contains at least nx + 1 points of some trajectory, where nx equals the number of connected components of T \ {x}. Then, for any open subset G w(f) in T, there exists a positive integer m = m(G) such that at most m points of any trajectory lie outside G.This result is a generalization of the related result for maps of the interval.
