Nonlocal Problems for Differential Inclusions in Hilbert Spaces

2014 ◽  
Vol 22 (3) ◽  
pp. 639-656 ◽  
Author(s):  
I. Benedetti ◽  
N. V. Loi ◽  
L. Malaguti



1997 ◽  
Vol 29 (1) ◽  
pp. 65-76
Author(s):  
Bui An Ton


Author(s):  
Zuomao Yan ◽  
Hongwu Zhang

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the main results.



2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Messaoud Bounkhel

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is,ẋ(t)∈F(t,x(t))a.e. onI,x(t)∈S,∀t∈I,x(0)=x0∈S, (*), whereSis a closed subset in a Banach space𝕏,I=[0,T],(T>0),F:I×S→𝕏, is an upper semicontinuous set-valued mapping with convex values satisfyingF(t,x)⊂c(t)x+xp𝒦,∀(t,x)∈I×S, wherep∈ℝ, withp≠1, andc∈C([0,T],ℝ+). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.







2006 ◽  
Vol 36 (3) ◽  
pp. 765-781
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan


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