Impulsive differential inclusions involving evolution operators in separable Banach spaces

• Дата: 2012
• Автори: Benchohra, M., Nieto, J. J., Ouahab, A., Беньчохра, М., Ньєто, Дж. Дж., Оахаб, А.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2012
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/2625
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We present some results on the existence of mild solutions and study the topological structure of the sets of solutions for the following first-order impulsive semilinear differential inclusions with initial and boundary conditions: $$y'(t) − A(t)y(t) \in F(t, y(t)) \text{for a.e.} t \in J\ \{t1,..., tm,...\},$$ $$y(t^+_k) − y(t^−_k) = I_k(y(t^−_k)),\quad k = 1,...,$$ $$y(0) = a$$ and $$y'(t) − A(t)y(t) \in F(t, y(t)) \text{for a.e.} t \in J\ \{t1,..., tm,...\},$$ $$y(t^+_k) − y(t^−_k) = I_k(y(t^−_k)),\quad k = 1,...,$$ $$Ly = a,$$ where $J = IR_+,\; 0 = t_0 < t_1