semilinear evolution inclusions
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Author(s):  
JinRong Wang ◽  
A. G. Ibrahim ◽  
D. O’Regan

AbstractThis paper is concerned with the controllability issue of fractional semilinear evolution inclusions with noninstantaneous impulses. Using weak sequentially closed graph operators, we establish sufficient conditions to guarantee controllability results. We do not assume that the semigroup is compact or we do not assume a compactness-type condition on the multivalued function. Finally, two examples are given to illustrate our theory.


2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Zhenhai Liu ◽  
Maojun Bin ◽  
Xiaoyou Liu

AbstractIn this paper, we research the existence of solutions for a class of Riemann-Liouville fractional evolution inclusions with nonconvex right hand side. Our main results obtain the existence of the extreme solution and the relationship of the solution sets between the original problem and the convexified problem. In the end, we give an example to illustrate the applications of the abstract results.


2016 ◽  
Vol 26 (2) ◽  
pp. 1365-1378 ◽  
Author(s):  
O. Cârjă ◽  
T. Donchev ◽  
A. I. Lazu

Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu

In this paper, we study the problem of the existence of solutions for a class of fractional semilinear evolution inclusions with non-convex right-hand side. We mainly focus on the existence of the extreme solution and the relationship of the solution sets between the original problem and the convexified problem. An example is provided to illustrate the application of the obtained theory.


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