含双参数的非线性二阶脉冲微分系统的正解

Positive Solutions for Nonlinear Second Order Impulsive Differential Systems with Two Parameters

摘要:

研究一类带有双参数的非线性二阶m点脉冲微分系统正解的存在性并讨论正解不存在的情况,其中非线性项可有不同性质,系数 a1(t)和 a2(t)均 Lp可积.通过构造一个特殊的锥,结合不动点指数理论,得到了参数 λ和 μ在不同条件下正解存在性定理,并在λ很小时得到了正解不存在性定理.

Abstract:

The paper presents a study of the existence of positive solutions for a class of nonlinear second order impulsive differential systems with two parameters and the nonexistence of positive solutions,where the nonlinear terms have different properties and their coefficients a1(t),a2(t) are LPintegrable.By applying the theory of the fixed point index and constructing a special cone,the existence theorem of positive solutions is proved when parameters λ and μ have different conditions,and the nonexistence theorem of positive solutions is proved while λ is sufficiently small.