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

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