Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 08, pp. 1-10.

Title: Existence and uniqueness of anti-periodic solutions
       for nonlinear third-order differential inclusions
        
Authors: Touma Haddad (Univ. de Jijel, Algerie)
         Tahar Haddad (Univ. de Jijel, Algerie)

Abstract:
 In this article, we study the existence  of anti-periodic
 solutions for the  third-order differential inclusion
 $$\displaylines{
 u'''(t)\in \partial\varphi(u'(t))+F(t,u(t))\quad \hbox{a.e. on }[0,T]\cr
 u(0)=-u(T), \quad u'(0)=-u'(T),\quad u''(0)=-u''(T),
 }$$
 where $\varphi$ is a proper convex, lower semicontinuous and even
 function, and F is an upper semicontinuous convex compact
 set-valued mapping. Also uniqueness of anti-periodic
 solution is studied.


Submitted September 28, 2012. Published January 09, 2013.
Math Subject Classifications: 34C25, 34G20, 49J52.
Key Words: Anti-periodic solution; differential inclusions; subdifferential.