无界函数 meaning in English
unbounded function
unlimited function
Examples
- On operators and approximation of unbounded continuous functions
算子与无界函数逼近 - 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
( ? ， ? )为r ~ n中内积， | ? |为对应范数。 f [ 0 ， t ] r ~ n r连续， ? f ( t ， x )存在且连续， h l ~ 1 ( 0 ， t ； r ~ n ) 。利用ekeland变分原理和鞍点定理讨论了该系统周期解的存在性，把非线性项和位势函数放宽到一类无界函数，推广了这方面工作的一些已有结果；利用广义鞍点定理和lusternik - schnirelman畴数理论得到了该系统的多重周期解，取掉了泛函的常定要求；最后利用对称山路定理得到没有扰动时系统的无穷多周期解。 - The second problem is the comparison principle on the full space . for the viscosity supsolution and subsolution v and u , we have the result u < u on the condition that lim finally , we investigate the compar - iaon principle for unbounded functions on the full space . when the equation ' s subsolution and supsolution u and v satisfy c is constant ) and the proper assumptions of the equation and the measure , we proved the comparison principle
第二个问题是全空间上的比较原理，对这类方程的上下解v和u ，只要，也有比较结果u v ，最后讨论全空间上无界函数的比较原理，当方程的上、下解低于一次增长，在对方程和测度的适当假设下，证明了粘性解的比较原理。