Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces

Semilinear nonlocal differential inclusions in Banach spaces

This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...

On Second-order Multivalued Impulsive Functional Differential Inclusions in Banach Spaces

Differential equations arise in many real world problems such as physics, population dynamics, ecology, biological systems, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. Much has been done under the assumption that the state variables and system parameters change continuously. However, one may easily visualize situations in nature where abrupt changes such...

Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces

Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces

and Applied Analysis 3 To prove our main results, for any h ∈ C J, E , we consider the Neumann boundary value problem NBVP of linear impulsive differential equation in E: −u′′ t Mu t h t , t ∈ J ′, −Δu′|t tk yk, k 1, 2, . . . , m, u′ 0 u′ 1 θ, 2.3 where M > 0, yk ∈ E, k 1, 2, . . . , m. Lemma 2.4. For any h ∈ C J, E , M > 0, and yk ∈ E, k 1, 2, . . . , m, the linear NBVP 2.3 has a unique soluti...

Global solutions for second order impulsive integro-differential equations in Banach spaces

This paper regards initial value problem for second order impulsive integro-differential equations as some nonlinear vector system. By means of the Mönch′s fixed point theorem, some existence theorems of solutions of the initial value problem are established. The results are newer than all of the previous ones because of the more general form compactness-type condition and the weaker restrictio...