The existence of positive solutions to neutral delay impulsive differential equations
This paper deals with neutral delay impulsive differential equations of the form NEWLINE\[NEWLINE\begin{aligned}\left[ x(t)+\sum \limits_{j=1}^{M}p_{j}(t)x(t-\tau _{j}(t))\right] ^{\prime }+\sum \limits_{i=1}^{N}q_{i}(t)x(t-\sigma _{i}(t)) &= 0,\quad t\neq t_{k},\\ \Delta \left[ x(t_{k})+\sum \limits_{j=1}^{M}p_{j}(t_{k})x(t_{k}-\tau _{j}(t_{k}))\right] +\sum \limits_{i=1}^{N}q_{i}(t_{k})x(t_{k}-\sigma _{i}(t_{k}))& = 0,\quad t=t_{k}.\end{aligned}NEWLINE\]NEWLINE By using the a generalized characteristic equation, sufficient conditions for the existence of positive solutions are obtained.
scientific article; zbMATH DE number 6082729