半正型四阶脉冲微分方程边值问题的正解

Positive Solutions to the Boundary Value Problem of a SemipositoneFourth-order Impulsive Differential Equation

运用不动点指数理论研究具有半正非线性项和脉冲项的四阶微分方程边值问题。将该问题转化为等价的积分方程,并构造合适的锥和全连续算子,在相关线性算子第一特征值条件下获得该问题正解的存在性,非线性项和脉冲项满足超线性增长,推广和改进了近期这方面的一些成果。

This paper uses the fixed point index theory to study the boundary value problem of a semipositone fourth-order impulsive differential equation.The problem is transformed into its equivalent integral equation,and suitable cones and fully continuous operators are constructed to obtain the existence of positive solutions under the first eigenvalue condition of the relevant linear operator.The nonlinearity and impulsive term grow superlinearly which improves recent achievements in the field.