Application of Pettis integration to delay second order differential inclusions
نویسندگان
چکیده
In this paper some fixed point 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 ü(t) ∈ F (t, u(t), u(h(t)), u̇(t)) +H(t, u(t), u(h(t)), u̇(t)) a.e. t ∈ [0, 1], where F is a convex valued multifunction upper semi continuous on E ×E ×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) ⊂ Γ1(t), H(t, x, y, z) ⊂ Γ2(t), where the multifunctions Γ1,Γ2 : [0, 1] ⇉ E are uniformlyPettis integrable . 2000 Mathematics subject Classification: 34A60, 28A25, 28C20.
منابع مشابه
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. 1 Correction In the above article, Proposition 2.2 is not true since the normed space P 1 E ([0, 1]) is not complete. Consequently, to corr...
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