potential infinity 中文意思是什麼
potential infinity
解釋
【數學】潛無窮。-
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。 -
The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils. because " the surface current source is placed at the interface, the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation. by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants, the expressions for the magnetic vector potential of the three regions are solved out
在求解過程中，假定放置式圓柱線圈是由無窮多個對稱圓環線圈密饒而成，首先求解含有有限長磁芯的通電對稱圓環線圈的電磁場：以有限長圓柱磁芯的側面和圓環線圈所在圓柱面為分界面將場域劃分為三個小區域，由於場源放置在內邊界面上，使得關于矢量磁位的非齊次約束方程轉化成齊次亥姆霍茲方程，利用分離變量法求解，根據分界面鄭州大學碩十研究生畢業論文摘要條件以及無限遠條件確定待定常數，從而得到各場區矢量磁位的表達式。
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