二阶奇异脉冲微分方程周期边值问题的正解

Positive Solutions of Periodic Boundary Value Problems for Singular Second Order Impulsive Differential Equation

二阶微分方程边值问题可描述两端支撑弹性梁的形变等一些问题,其广泛的应用引起很多学者的关注.本文研究二阶周期边值问题,其中非线性项在端点处具有奇异性(非线性项可有不同的超次线性).通过构造一个特殊的锥,利用不动点指数定理得到了该问题的正解.最后给出一个例子说明主要结果.

Some problems like the deformations of a two-end supported elastic beam can be described by a second order differential equation boundary value problem. Its wide applications have attracted much attention of researchers. In this paper, we study the second order periodic boundary value prob- lems for the case that the nonlinear terms are singular at the endpoints （the nonlinear terms may have different superlinearity and sublinearity）. Multiple positive solutions to this problem are achieved by constructing a special cone and using the fixed point index theorem. Finally, an example is given to illustrate the main results.