不动点指数理论在多脉冲微分方程中的应用

Application of Fixed Point Index Theory in Impulsive Differential Equation with Multiple Pulses

利用Banach空间中的不动点指数理论,并结合锥理论和Leray-Schauder度理论,对一类非线性算子方程建立了多重变号解存在性定理,然后将所获结论应用到含多个脉冲情形的微分方程两点边值问题上,得到了多个变号解存在的结论.

Using fixed point index theory in Banach space,cone theory,and Leray-Schauder degree theory,the existence and multiplicity of signchanging solutions for a class of nonlinear operator equations was studied.By applying the above conclusions in impulsive differential equations for two-point boundary value problems with multiple pulses,the existence of sign-changing solutions was proved.