scholarly journals Differential Equations with Fuzzy Parameters via Differential Inclusions

2001 ◽  
Vol 255 (1) ◽  
pp. 177-194 ◽  
Author(s):  
Tadeusz Rzeżuchowski ◽  
Janusz Wąsowski
Keyword(s):  
Differential Equations ◽  
Differential Inclusions ◽  
Fuzzy Parameters

Nonconvex Differential Inclusions with Nonlinear Monotone Boundary Conditions

1997 ◽  
Vol 4 (6) ◽  
pp. 501-508
Author(s):  
S. A. Brykalov
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Differential Inclusions ◽  
Nonlinear Boundary ◽  
Functional Differential Equations ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Selection Theorem ◽  
Functional Differential ◽  
Nonconvex Differential Inclusions

Abstract Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo.

scholarly journals A Differential Algebraic Method to Approximate Nonsmooth Mechanical Systems by Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaogang Xiong ◽  
Ryo Kikuuwe ◽  
Motoji Yamamoto
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Dry Friction ◽  
Differential Inclusions ◽  
Mechanical Systems ◽  
Algebraic Method ◽  
Unilateral Contact ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Simulation Results

Nonsmooth mechanical systems, which are mechanical systems involving dry friction and rigid unilateral contact, are usually described as differential inclusions (DIs), that is, differential equations involving discontinuities. Those DIs may be approximated by ordinary differential equations (ODEs) by simply smoothing the discontinuities. Such approximations, however, can produce unrealistic behaviors because the discontinuous natures of the original DIs are lost. This paper presents a new algebraic procedure to approximate DIs describing nonsmooth mechanical systems by ODEs with preserving the discontinuities. The procedure is based on the fact that the DIs can be approximated by differential algebraic inclusions (DAIs), and thus they can be equivalently rewritten as ODEs. The procedure is illustrated by some examples of nonsmooth mechanical systems with simulation results obtained by the fourth-order Runge-Kutta method.

scholarly journals A note on multivalued differential equations on proximate retracts

1999 ◽  
Vol 12 (2) ◽  
pp. 169-178 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Nonlinear Alternative ◽  
Existence Criteria ◽  
Bouligand Cone ◽  
Multivalued Differential Equations

This paper discusses viable solutions for differential inclusions in Banach spaces. Existence will be established in two steps. In step 1, a nonlinear alternative of Leray-Schauder type [8] for maps with closed graphs will be used to establish a variety of existence principles for the Cauchy differential inclusion. Step 2 involves using the results in step 1 together with some tricks involving the Bouligand cone (and sometimes the Urysohn function) so that new existence criteria can be established for multivalued differential equations on proximate retracts.

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.

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