In this paper, we consider two problems （MR） and （MH）.Let L<sub>1j</sub>（j=1, …, m） be a mutually exclusive closed Lyapunov curve system in the upper half-planeZ<sup>+</sup> and each cur...In this paper, we consider two problems （MR） and （MH）.Let L<sub>1j</sub>（j=1, …, m） be a mutually exclusive closed Lyapunov curve system in the upper half-planeZ<sup>+</sup> and each curve L<sub>1j</sub> take the clockwise direction as its positive direction, D<sub>1j</sub><sup>-</sup> be the inner region boundedby L<sub>2j</sub>（j=1,…,m） and L<sub>1</sub>= L<sub>1j</sub>, D<sub>1</sub><sup>+</sup>=Z<sup>+</sup>\（D<sub>1</sub><sup>-</sup> U L<sub>1</sub>）, X be the real axis, {a<sub>1</sub>,b<sub>1</sub>…,a<sub>n</sub>,b<sub>n</sub>} be a set of points on X and -∞【a<sub>1</sub>【b<sub>2</sub>【…【a<sub>n</sub>【b<sub>n</sub>【+∞, <sub>k</sub>（x）,ψ<sub>k</sub>（x） be some given re-al-valued functions in （a<sub>k</sub>, b<sub>k</sub>） , (b<sub>k</sub>, a<sub>k+1</sub>) , ∈H, respectively. For simplification, let a<sub>n+1</sub>=a<sub>1</sub> and ψ<sub>n</sub> （x） =0,x∈ (b<sub>n</sub>,a<sub>n+1</sub>)=（-∞,a<sub>1</sub>） ∪ （b<sub>n</sub>,+∞）.展开更多
基金The project is supported by the Natural Science Foundation of Fujian
文摘In this paper, we consider two problems （MR） and （MH）.Let L<sub>1j</sub>（j=1, …, m） be a mutually exclusive closed Lyapunov curve system in the upper half-planeZ<sup>+</sup> and each curve L<sub>1j</sub> take the clockwise direction as its positive direction, D<sub>1j</sub><sup>-</sup> be the inner region boundedby L<sub>2j</sub>（j=1,…,m） and L<sub>1</sub>= L<sub>1j</sub>, D<sub>1</sub><sup>+</sup>=Z<sup>+</sup>\（D<sub>1</sub><sup>-</sup> U L<sub>1</sub>）, X be the real axis, {a<sub>1</sub>,b<sub>1</sub>…,a<sub>n</sub>,b<sub>n</sub>} be a set of points on X and -∞【a<sub>1</sub>【b<sub>2</sub>【…【a<sub>n</sub>【b<sub>n</sub>【+∞, <sub>k</sub>（x）,ψ<sub>k</sub>（x） be some given re-al-valued functions in （a<sub>k</sub>, b<sub>k</sub>） , (b<sub>k</sub>, a<sub>k+1</sub>) , ∈H, respectively. For simplification, let a<sub>n+1</sub>=a<sub>1</sub> and ψ<sub>n</sub> （x） =0,x∈ (b<sub>n</sub>,a<sub>n+1</sub>)=（-∞,a<sub>1</sub>） ∪ （b<sub>n</sub>,+∞）.
