含双参数的非线性二阶脉冲微分系统的正解

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.

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

The existence of positive solutions is studied for a class of nonlinear second order impulsive differential systems with two parameters, the nonexistence results are talked about as well, where the nonlinear terms have different properties and their coefficients $a_1(t)$, $a_2(t)$ are L$^{mathrm{P}}$ -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 $lambda$ and $mu$ have different conditions, and the nonexistence theorem of positive solutions is proved while $lambda$ is sufficiently small.