Application of Pettis integration to delay second order differential inclusions

In this paper some fixed principle is applied to prove, in a separable Banach space, the existence of solutions for delayed second order differential inclusions with three-point boundary conditions of the form $$\ddot u(t)\in F(t,u(t),u(h(t)),\dot u(t))+H(t,u(t),u(h(t)),\dot u(t))a.e.t\in [0,1],$$ where $F$ is a convex valued multifunction upper semecontinuous on $E\times E\times E$, $H$ is a lower semicontinuous multifunction and $h$ is a bounded and continuous mapping on $[0,1]$. The existence of solutions is obtained under the assumptions that $F(t,x,y,z)\subset \Gamma_1(t)$, $H(t,x,y,z)\subset \Gamma_2(t)$, where the multifunctions $\Gamma_1, \Gamma_2:[0,1]\rightrightarrows E$ are uniformly Pettis integrable

Corrigendum to Application of Pettis integration to delay second order differential inclusions

This paper serves as a corrigendum to the paper titled Application of Pettis integration to delay second order differential inclusions appearing in EJQTDE no. 88, 2012. We present here a corrected version of Theorem 3.1, because Proposition 2.2 is not true

On perturbed sweeping process

Artículo de publicación ISISin acceso a texto completoThis paper is devoted to the study of a perturbed differential inclusion governed by a sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition and a scalarly upper semicontinuous set-valued map