Existence theory for semilinear evolution inclusions involving measures

2016 ◽  
Vol 290 (7) ◽  
pp. 1004-1016
Author(s):  
Mieczysław Cichoń ◽  
Bianca Satco
Keyword(s):  
Existence Theory ◽  
Evolution Inclusions ◽  
Semilinear Evolution Inclusions

Controllability of Fractional Evolution Inclusions with Noninstantaneous Impulses

2018 ◽  
Vol 19 (3-4) ◽  
pp. 321-334 ◽  
Author(s):  
JinRong Wang ◽  
A. G. Ibrahim ◽  
D. O’Regan
Keyword(s):  
Sufficient Conditions ◽  
Multivalued Function ◽  
Type Condition ◽  
Closed Graph ◽  
Evolution Inclusions ◽  
Semilinear Evolution Inclusions ◽  
Noninstantaneous Impulses

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.

On the ‘bang-bang’ principle for a class of fractional semilinear evolution inclusions

2014 ◽  
Vol 144 (2) ◽  
pp. 333-349 ◽  
Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu
Keyword(s):  
Original Problem ◽  
Existence Of Solutions ◽  
Evolution Inclusions ◽  
Solution Sets ◽  
Right Hand ◽  
Semilinear Evolution Inclusions ◽  
Relationship Of ◽  
The Relationship ◽  
Extreme Solution

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.

On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions

2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Zhenhai Liu ◽  
Maojun Bin ◽  
Xiaoyou Liu
Keyword(s):  
Original Problem ◽  
Existence Of Solutions ◽  
Evolution Inclusions ◽  
Solution Sets ◽  
Right Hand ◽  
Semilinear Evolution Inclusions ◽  
Relationship Of ◽  
The Relationship ◽  
Extreme Solution

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.

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