Functional Evolution Equations with Nonconvex Lower Semicontinuous Multivalued Perturbations

Multivalued Semilinear Neutral Functional Differential Equations with Nonconvex-valued Right-hand Side

Existence Results for Impulsive Functional and Neutral Functional Differential Inclu- Sionswith Lower Semicontinuous Righthand Side

In this paper, Schaefer’s fixed point theorem combined with a selection theorem due to Bressan and Colombo is used to investigate the existence of solutions for first and second order impulsive functional and neutral differential inclusions with lower semicontinuous and nonconvex-valued right-hand side.

Attractors for Nonautonomous Multivalued Evolution Systems Generated by Time-dependent Subdifferentials

In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations. In this paper, we treat the multivalued dynamical systems associated with time-dependent subdifferentials, in which the solution is not unique for a given initial state. In particular, we discuss the asymptotic behaviour of o...

Viable Solutions for Second Order Nonconvex Functional Differential Inclusions

We prove the existence of viable solutions for an autonomous second-order functional differential inclusions in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the subdifferential of a proper lower semicontinuous convex function.

General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations

We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: −A x 3 t ∈ N K t, ẋ t ; A ẍ t F t, x t , ẋ t , ẍ t G x t , ẋ t , ẍ t a.e. 0, T , A ẍ t ∈ K t, ẋ t , a.e. t ∈ 0, T , x 0 x0, ẋ 0 u0, ẍ 0 υ0, where T > 0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-v...