Electron. J. Diff. Equ., Vol. 2013 (2013), No. 08, pp. 1-10.

Existence and uniqueness of anti-periodic solutions for nonlinear third-order differential inclusions

Touma Haddad, Tahar Haddad

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.

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Touma Haddad
Département de Mathématiques, Faculté des Sciences
Université de Jijel, B.P. 98, Algérie
email: touma.haddad@yahoo.com
Tahar Haddad
Laboratoire LMPA, Faculté des Sciences
Université de Jijel, B.P. 98, Algérie
email: haddadtr2000@yahoo.fr

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