Existence of solution for impulsive differential equations with indefinite linear part
The authors consider the impulsive boundary value problem \[ \begin{aligned} &-u''(t) = f(t,u(t)), \quad t \in [0,1]\setminus\{t_1,\ldots,t_m\},\\ &u(0) = u(1) = 0, \\ &u'(t_j+) = u'(t_j-) - I_j(u(t_j)), \quad j=1,\ldots,m, \end{aligned} \] where \(m \in N\), \(0 < t_1 < t_2 < \ldots < t_m < 1\), \(f\) is a Carathéodory function on \((0,1)\times \mathbb{R}\), \(I_j : \mathbb{R} \to \mathbb{R}\) are continuous functions. Using critical point theory (Saddle Point Theorem), the existence of at least one solution for the non-resonant case is proved.
scientific article; zbMATH DE number 6518555
scientific article