Abstract and Applied Analysis

Relaxation Problems Involving Second-Order Differential Inclusions

Adel Mahmoud Gomaa

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Abstract

We present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, u ¨ ( t ) F ( t , u ( t ) , u ˙ ( t ) ) a.e. on [ 0,1 ] ; u ( 0 ) = 0 , u ( η ) = u ( θ ) = u ( 1 ) and, with m 3 boundary conditions, u ¨ ( t ) F ( t , u ( t ) , u ˙ ( t ) ) a.e. on [ 0,1 ] ; u ˙ ( 0 ) = 0 , u ( 1 ) = i = 1 m - 2 a i u ( ξ i ) , where 0 < η < θ < 1 , 0 < ξ 1 < ξ 2 < < ξ m - 2 < 1 and F is a multifunction from [ 0,1 ] × n × n to the nonempty compact convex subsets of n . We have results that improve earlier theorems.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 792431, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511840

Digital Object Identifier
doi:10.1155/2013/792431

Mathematical Reviews number (MathSciNet)
MR3044990

Zentralblatt MATH identifier
1272.49025

Citation

Gomaa, Adel Mahmoud. Relaxation Problems Involving Second-Order Differential Inclusions. Abstr. Appl. Anal. 2013 (2013), Article ID 792431, 9 pages. doi:10.1155/2013/792431. https://projecteuclid.org/euclid.aaa/1393511840


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