Multiple positive solutions for first-order impulsive integrodifferential equations on the half line in Banach spaces (Q762970)

The author considers the existence of multiple positive solutions for first-order impulsive integrodifferential equations on the half line in a real Banach space \(E\): \[ \begin{aligned} & u' (t) = f (t,u(t), (Tu) (t), (Su) (t)), \\ &\Delta u |_{t=t_k} = i_k (u(t_k)), \quad k= 1,2.3. \dots, \\ &u (\infty) = \gamma u(\mu) + \beta u (0),\end{aligned} \] where \[ \begin{aligned} (Tu) (t) = \int^t_0 K (t,s ) u (s) ds,\\ (Su) (t) = \int^\infty_0 H (t,s) u (s) ds. \end{aligned} \] Fixed point theorems of cone expansion are used. A new cone is introduced. Two examples are given.