Existence of solutions for non-autonomous second-order stochastic inclusions with Clarke’s subdifferential and non instantaneous impulses

Existence of Solution for a Second-Order Neutral Differential Equation with State Dependent Delay and Non-instantaneous Impulses

Abstract: In this paper existence of mild solution of a class of second order partial neutral differential equation with state dependent delay and non-instantaneous impulses is investigated. Hausdorff measure of noncompactness and Darbo Sadovskii fixed point theorem are used to prove the existence. Also, some restrictive conditions such as the compactness assumption on the associated cosine or ...

Existence of Mild Solutions to Partial Differential Equations with Non-instantaneous Impulses

In this article, we study the existence of piecewise-continuous mild solutions for the initial value problems for a class of semilinear evolution equations. These equations have non-instantaneous impulses in Banach spaces and the corresponding solution semigroup is noncompact. We assume that the nonlinear term satisfies certain local growth condition and a noncompactness measure condition. Also...

Duality Mappings and the Existence of Periodic Solutions for Non-autonomous Second Order Systems

is a vector version of p-Laplacian operator. In order to say what we understand by solution for the problem (1.1), (1.2) we remind some basic results concerning the W 1,p T -spaces. Let C T be the space of indefinitely differentiable T -periodic functions from R to R . We denote by 〈·, ·〉 the inner product on R and by ‖ · ‖, the norm generated by this inner product (the same meaning is applied ...

New existence and multiplicity theorems of periodic solutions for non-autonomous second order Hamiltonian systems

In the present paper, the non-autonomous second order Hamiltonian systems { ü(t) = ∇F(t, u(t)), a.e. t ∈ [0, T ] u(0)− u(T ) = u̇(0)− u̇(T ) = 0, (1) are studied and a new existence theorem and a new multiplicity theorem of periodic solutions are obtained. c © 2007 Elsevier Ltd. All rights reserved.

Periodic Solutions of a Class of Non-autonomous Second-order Differential Inclusions Systems