周期扰动的非保守系统的周期解的存在性与唯一性

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR PERIODICALLY PERTURBED NON-CONSERVITIVE SYSTEMS

考虑具有周期扰动的Linard型非保守系统 +C+gradG(x)=p(t),其中C是n×n的实对称方阵,x=(x_1,x_2,…x_n)~T∈R^n,G∈C^2(R^n,R),p∈C(R,R^n)且p(t+ω)≡p(t),ω>0是常数,利用重合度理论讨论周期解的存在性与唯一性,得到了苦干简便的判别条件。

Consider the periodically perturbed non-conservitive systems of Lienard type where C is n×n real symmetry matrix, x = (x1, x2, … , xn)T, G ∈ C2(Rn, R), p ∈ C(R, Rn), p(t+w) = p(t), w > 0. By using conincidence degree theory, the authors discuss the existence and uniqueness of periodic solutions and obtain some new effective results.