Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions

Abstract

According to theories for integrated semigroups and Leray-Schauder theorem of the alternative for Kakutani maps, this paper is mainly concerned with existence results for some non-densely defined impulsive neutral functional differential inclusions with nonlocal conditions in Banach spaces. An example is also given to illustrate the obtained theorem.

Existence Results for Impulsive Systems With Nonlocal Conditions in Banach Spaces

“…. , p. In the past several years theorems about existence, uniqueness of differential and impulsive functional differential abstract evolution Cauchy problem with nonlocal conditions have been studied by Byszewski and Lakshmikantham [4], by Akca et al [1], by Anguraj et al [2], by Fu et al [9,10] and by Chang et al [6] and the references therein. This paper has four sections.…”

Existence results for impulsive differential equations with nonlocal conditions via measures of noncompactness

“…For more details about nondensely defined operators and integrated semigroups we refer to [13,16,21].…”

“…[6,7,8,13,17,18,19,23,28]. It is more precise for describing nature phenomena than the classical condition since more information is taken into account, thereby decreasing the negative effects incurred by a possibly erroneous single measurement taken at the initial time.…”

Existence results for semilinear differential equations with nonlocal and impulsive conditions

“…Recently, the theory of impulsive differential and partial differential equations has become an important area of investigation because of its wide applicability in control, mechanics, electrical engineering fields and so on. For more details on this theory and on its applications we refer to the monographs Benchohra et al [6], Lakshmikantham et al [17], the papers of [1,[8][9][10]15,16,[19][20][21]25] and references therein.…”