二阶周期边值问题正解的存在性

Existence of Positive Solutions to Second Order Ordinary Differential Systems with Periodic Boundary Value

周期边值问题已成为方程研究领域的一个重要分支,它在许多实际问题中有着更为广泛的应用,本文主要研究了二阶周期边值问题正解的存在性.利用锥上不动点指数理论研究了二阶周期边值问题方程组的正解的存在性,通过相应的线性问题的第一特征值和拓扑度乘积定理,建立了正解的存在性定理.最后,我们给出具体的例子说明了该正解存在性定理的结论.

The periodic boundary value problem has been an important area of investigation and it has been applied in a lot of practical problems.We mainly discuss in this paper the positive solutions to the second order ordinary differential systems with periodic boundary value.We obtain the existence of the positive solutions to the second order ordinary differential systems with periodic boundary value by employing the fixed-point theory,and establish the existence theorems of the positive solutions by using the first eigenvalue of the corresponding linear problem and the product of topology degree.Finally,we present an example to demonstrate the existence theorems of the positive solutions.