African Diaspora Journal of Mathematics

Topological Structure of the Solutions Set of Impulsive Semilinear Differential Inclusions with Nonconvex Right-Hand Side

M. Benchohra, J. J. Nieto, and A. Ouahab

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we study the topological structure of solution sets for the following first-order impulsive evolution inclusion with initial conditions: $$ \left\{ \begin{array}{rlll} y'(t)-Ay(t) &\in& F(t,y(t)), &\hbox{ a.e. } \, t\in J\backslash \{t_{1},\ldots,t_{m}\},\\ y(t^+_{k})-y(t^-_k)&=&I_{k}(y(t_{k}^{-})), &k=1,\ldots,m\\ y(0)&=&a\in E, \end{array} \right. $$where $J:=[0,b]$ and $0 = t_0 < t_1 < \,... \,< t_m < b$, $A$ is the infinitesimal generator of a $C_0-$semigroup of linear operator $T(t)$ on a separable Banach space $E$ and $F$ is a set-valued map. The functions $I_k$ characterize the jump of the solutions at impulse points $t_k$ ($k=1, \ldots ,m$). The continuous selection of the solution set is also investigated.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 16, Number 2 (2014), 72-91.

Dates
First available in Project Euclid: 20 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1413809904

Mathematical Reviews number (MathSciNet)
MR3270008

Zentralblatt MATH identifier
1332.34103

Subjects
Primary: 34A37: Differential equations with impulses 34A60: Differential inclusions [See also 49J21, 49K21] 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

Keywords
Impulsive differential inclusions semigroup solution set compactness absolute retract

Citation

Benchohra, M.; Nieto, J. J.; Ouahab, A. Topological Structure of the Solutions Set of Impulsive Semilinear Differential Inclusions with Nonconvex Right-Hand Side. Afr. Diaspora J. Math. (N.S.) 16 (2014), no. 2, 72--91. https://projecteuclid.org/euclid.adjm/1413809904


Export citation