second saddle 中文意思是什麼
second saddle
解釋
副座板-
Existence of periodic solutions with saddle point characteristics for some non - autonomous second order systems
某類非自治二階系統具鞍點特徵的周期解的存在性 -
The paper is concerned with periodic solutions to nonautonomous second order hamilton systems where, m : [ 0, t ] - s ( rn, rn ) is a continuous mapping in the space s ( rn, rn ) of symmetric real ( n x n ) - matrices, such that for some u > 0 and all ( t, z ) [ 0, t ] x rn, ( m ( t ) x, x ) > u | x | 2. a s ( rn, rn ), f : [ 0, t ] x rn r is continuous and f : [ 0, t ] xr r exists, is continuous and we study the existence of periodic solutions of the systems by using ekeland variational principle and the saddle points theorem. we suppose that the nonlinearity vf and potential f belongs to a class of unbounded functional. our work improves the existed results. we obtained the results of multiplicity of periodic solutions of the systems by using lusternik - schnirelman category theory and the generalized saddle points theorem, and the functional does not need the condition of constant definite. at last, we obtained the existence of infinity many distinct periodic solutions of the corresponding non - perturbation systems by using the symmetric mountain pass theorem
（ ? ， ? ）為r ~ n中內積， | ? |為對應范數。 f [ 0 ， t ] r ~ n r連續， ? f （ t ， x ）存在且連續， h l ~ 1 （ 0 ， t ； r ~ n ） 。利用ekeland變分原理和鞍點定理討論了該系統周期解的存在性，把非線性項和位勢函數放寬到一類無界函數，推廣了這方面工作的一些已有結果；利用廣義鞍點定理和lusternik - schnirelman疇數理論得到了該系統的多重周期解，取掉了泛函的常定要求；最後利用對稱山路定理得到沒有擾動時系統的無窮多周期解。 -
At first, we introduce a class of generalized s - r - kkm type mapping in g - convex space, and establish generalized s - r - kkm type nonempty intersection theorem under the noncompact setting of g - convex space. as for application, some new minimax inequalities, saddle point theorem and existence theorem of maximal elements are proved in g - convex spaces ; second, by using the generalized r - kkm mapping and generalized r - kkm theorems in [ 13 ], some new existence theorem of maximal elements, existence theorem of equilibrium point for the abstract generalized vector equilibrium problem and existence theorem of solutions for equilibrium problem with lower and upper bounds are obtained in topological spaces
首先，我們在g -凸空間內引入了廣義s - r - kkm型映像，並在非緊設置下建立了一類新的廣義s - r - kkm型非空交定理，作為應用，證明了g -凸空間內一些新的極大極小不等式、鞍點定理和極大元存在定理；其次，利用文[ 13 ]中引入的廣義r - kkm映像和廣義r - kkm定理，在拓撲空間上得到了一些新的極大元存在定理、抽象廣義矢量平衡問題平衡點的存在定理和有上下界的平衡問題解的存在性定理。 -
In the second part, we try to apply orthogonal polynomial approximations to the dynamical response problem of the duffing equation with random parameters under harmonic excitations. we first reduce the random duffing system into its non - linear deterministic equivalent one. then, using numerical method, we study the elementary non - linear phenomena in the system, such as saddle - node bifurcation, symmetry break bifurcation, phenomena in the system, such as saddle - node bifurcation, symmetry break bifurcation, period - doubling bifurcation and chaos
本文第二部分嘗試將正交多項式逼近方法應用於隨機duffing系統，提出與之等價的確定性非線性系統的新概念，並用數值方法對該系統在諧和激勵下的鞍結分叉、對稱破裂分叉、倍周期分叉、和混沌等各種基本非線性響應進行了初步探討。
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