• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.137-154
• /
• 2007

In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.

• 대한수학회지
• /
• 제41권2호
• /
• pp.295-308
• /
• 2004

In this paper, we prove the existence of integral solutions, defined on a compact interval, for functional differential inclusion with nonlocal conditions and impulsive functional differential inclusions in a Banach space.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제24권2호
• /
• pp.229-242
• /
• 2020

Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.

• Kyungpook Mathematical Journal
• /
• 제48권1호
• /
• pp.1-14
• /
• 2008

In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.57-69
• /
• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.