摘要
存在多个(无穷多个)调和解的条件,其中x∈R^n,F∈C^2(R^n,R),G∈C^2(R^n,R),p∈C^0(R,R^n),且p(t+T)≡p(t),integral from n=1 to p(t)dt=0。 对高维非线性非自治系统调和解的讨论,通常都要给出条件,保证周期解只在一个有界集内存在,然后对包含上述有界集的有界凸域利用不动点原理证明调和解的存在性。这样的处理方法很难对调和解的个数问题作深入讨论。
By calculating the Leray-Schauder degrees of a completely continuous operator on different bounded convex domains in the Banaeh space of n-dimensional periodic continuous functions,this paper gives sufficient conditions for the existence of multiple and infinitely many harmonic solutions of vectorial Lienard equations.
出处
《应用数学学报》
CSCD
北大核心
1992年第4期541-549,共9页
Acta Mathematicae Applicatae Sinica
