New result for a class of impulsive differential equation with integral boundary conditions
The authors consider the impulsive boundary value problem \[ \begin{aligned} y''(t)& = f(t,y(t)), \quad 0 < t < 1,\quad t \neq t_k,\\ \triangle y|_{t=t_k} &= I_k(y(t_k)), \quad k = 1,\dotsc, n,\\ \triangle y'|_{t=t_k} &= \bar I_k(y(t_k),y'(t_k)), \quad k = 1,\dotsc,n,\\ y(0) - ay'(0) &= \int_0^1 g_0(s)y(s)\, \text{d}s,\\ y(1) - by'(1) &= \int_0^1 g_1(s)y(s)\, \text{d}s, \end{aligned} \] where \(0 < t_1 < \dotsb < t_n < 1\), \(f\), \(I_k\), \(\bar I_k\), \(g_0\), \(g_1\) are continuous, \(a,b \geq 0\). Using Krasnosel'skii's fixed point theorem, sufficient conditions ensuring the existence of positive solutions are obtained.
scientific article; zbMATH DE number 6130737