例句與用法

1. 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(nèi)積，|?|為對應(yīng)范數(shù)。f[0，t]r~nr連續(xù)，?f(t，x)存在且連續(xù)，hl~1(0，t；r~n)。利用ekeland變分原理和鞍點定理討論了該系統(tǒng)周期解的存在性，把非線性項和位勢函數(shù)放寬到一類無界函數(shù)，推廣了這方面工作的一些已有結(jié)果；利用廣義鞍點定理和lusternik-schnirelman疇數(shù)理論得到了該系統(tǒng)的多重周期解，取掉了泛函的常定要求；最后利用對稱山路定理得到?jīng)]有擾動時系統(tǒng)的無窮多周期解。