| A STRONG RESONANCE PROBLEM |
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| 作者姓名： | Zhang Gongqing Liu Jiaquan |
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| 作者单位： | Institute of Mathematics Beijing University，Department of Mathematics Graduate School Academia Sinica Beijing China.，Beijing China. |
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| 摘 要： | Consider a functional f(x, v)=(Ax, x)/2+G(x, v), defined on a product space H×V. where H is a Hilbert space and V is a compact manifold. Suppose that the linear part (Ax, x) is at resonance. In this paper, the strong resonance problem is studied in the variational approach, the existence of at least, cuplength V+1 critical points of f is proved. The abstract theorems are then applied to the existence problems of solutions for elliptic boundary value problems and Hamiltonian systems.
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| 收稿时间： | 7/3/1989 12:00:00 AM |
A Strong Resonance Problem |
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| Zhang Gongqing,Liu Jiaquan.A STRONG RESONANCE PROBLEM[J].Chinese Annals of Mathematics,Series B,1990,11(2):191-210. |
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| Authors: | Zhang Gongqing and Liu Jiaquan |
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| Institution: | Institute of Mathematics, Beijing University, Beijing, China. and Department of Mathematics, Graduate School, Academia Sinica, Beijing, China. |
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| Abstract: | Consider a functional f(x, v)=(Ax,x)/2+G(x,v), defined on a product space HxV, where H is a Hilbert space and V is a compact manifold. Suppose that the linear part (Ax, x) is at resonance. In this paper, the strong resonance problem is studied in the variational approach, the existence of at least, cuplength V+l critical points of f is proved. The abstract theorems are then applied to the existence problems of solutions for elliptic boundary value problems and Hamiltonian systems. |
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