2p和2q阶微分方程组正解的存在性

The Existence of Positive Solution for 2P-Order and 2Q-Order Nonlinear Ordinary Differential Systems

利用拓扑度乘积理论研究2p和2q阶非线性高阶微分方程组边值问题,通过相应的线性问题的第一特征值和拓扑度乘积理论建立了其正解的存在性定理,给出了利用特征值刻划的较为本质的结果,且突破了以往文献要求的方程组同阶和非线性项同是次线性或超线性的要求.

In this paper,by using the Product of topology degree theory,we study the problem of the 2p-order and 2q-order nonlinear ordinary differential systems with Dirichlet boundary value.The existence theorem on poisitive solution is established by using the first eigenvalue of the correspondind linear problems and theorem for product of topology degree. This paper gives a more essential result by using eigenvalue,which do not require that the nonlinear terms are superlinear or sublinear at ends（zero or infinty） and systems must have the same order.