scholarly journals Multi-point boundary value problems for lower semicontinuous differential inclusions

2002 ◽  
Vol 3 (2) ◽  
pp. 91
Author(s):  
Mouffak Benchohra ◽  
Sotiris K. Ntouyas
Keyword(s):  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Lower Semicontinuous ◽  
Boundary Value ◽  
Point Boundary

ON THE SOLUTION SETS OF FOUR-POINT BOUNDARY VALUE PROBLEMS FOR NONCONVEX DIFFERENTIAL INCLUSIONS

2011 ◽  
Vol 08 (01) ◽  
pp. 23-37 ◽  
Author(s):  
ADEL MAHMOUD GOMAA
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Boundary Value ◽  
Point Boundary ◽  
Boundary Problems ◽  
Solution Sets ◽  
Nonempty Compact ◽  
Nonconvex Differential Inclusions

We consider the multivalued problem [Formula: see text] under four boundary conditions u(0) = x0, u(η) = u(θ) = u(T) where 0 < η < θ < T and for F is a multifunctions from [0, T] × ℝn × ℝn to the nonempty compact subsets of ℝn not necessary convex. We give a lemma which is useful in the study of four boundary problems for the differential equations and the differential inclusions. Further we have results that improve earlier theorems.

scholarly journals On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds

2003 ◽  
Vol 2003 (10) ◽  
pp. 591-600 ◽  
Author(s):  
Yuri E. Gliklikh ◽  
Andrei V. Obukhovskii
Keyword(s):  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
Differential Inclusions ◽  
Extreme Values ◽  
Existence Theorems ◽  
Lower Semicontinuous ◽  
Boundary Value ◽  
Second Order ◽  
Configuration Spaces ◽  
Point Boundary

We consider second-order differential inclusions on a Riemannian manifold with lower semicontinuous right-hand sides. Several existence theorems for solutions of two-point boundary value problem are proved to be interpreted as controllability of special mechanical systems with control on nonlinear configuration spaces. As an application, a statement of controllability under extreme values of controlling force is obtained.

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