Existence of solutions for a second-order differential equation with non-instantaneous impulses and delay

Existence of mild solutions to partial neutral differential equations with non-instantaneous impulses

“…If t r ∈ (t k , s k ], k = 1, 2, · · · , n, then by (2.1), (3.3) and assumptions (H 3 ), we obtain (Gx r )(t r ) = γ k (t r , x r (t r )) 8) where N = max k=1,2,··· ,n sup t∈ D γ k (t r , 0) .…”

“…In 2013, Pierri et al [20] studied the existence of mild solution for a class of semi-linear abstract differential equation with non-instantaneous impulses by using the theory of analytic semigroup. By a compactness criterion a certain class of functions, Colao et al [8] investigated the existence of solutions for a second-order differential equations with noninstantaneous impulses and delay on an unbounded interval. Using the theory of semigroup and fixed point methods, Yu and Wang [25] discussed the existence of solution to periodic boundary value problems for nonlinear evolution equation with non-instantaneous impulses on Banach space.…”

“…Using the theory of semigroup and fixed point methods, Yu and Wang [25] discussed the existence of solution to periodic boundary value problems for nonlinear evolution equation with non-instantaneous impulses on Banach space. The motivation of this article is as follows: to the best of the authors knowledge, (see, for example [5,8,11,20,23]) used various fixed point theorems to study the existence results of evolution equations with non-instantaneous impulses when the corresponding semigroup U(t)(t ≥ 0) is compact, this is convenient to the equations with compact resolvent. But for this occurrence that the corresponding semigroup U(t)(t ≥ 0) is noncompact.…”

Variational approach to the existence of solutions for non-instantaneous impulsive differential equations with perturbation

“…Many classical methods can be used to study the non-instantaneous impulsive differential equations, such as theory of Analytic Semigroup, Fixed-Point theory [6,7,12,13] and so on. For some recent works on this type equation, we refer the readers to [1,4,5,10,11,[15][16][17].…”

Variational approach to non-instantaneous impulsive nonlinear differential equations

“…The existence of solutions of non-instantaneous impulsive problem has been studied via some approaches, such as fixed point theory and theory of analytic semigroup, see, for example, [5,7,11,12]. Recently, the variational structure of non-instantaneous impulsive linear problem has been developed in [3].…”