semicontinuous multifunctions
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Author(s):  
Yang-Yang Yu ◽  
Rong-Nian Wang ◽  
Ioan I. Vrabie

This paper deals with a nonlinear Volterra delay evolution inclusion subjected to a nonlocal implicit initial condition. The evolution inclusion involves an $m$-dissipative operator (possibly multivalued and/or nonlinear) and a noncompact interval. We first consider the evolution inclusion subjected to a local initial condition and prove an existence result for bounded $C^0$-solutions. Then, using a fixed point theorem for upper semicontinuous multifunctions with contractible values, we obtain a global solvability result for the original problem. Finally, we present an example to illustrate the abstract result.


Heliyon ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. e05367
Author(s):  
Chawalit Boonpok

2018 ◽  
Vol 38 (2) ◽  
pp. 147-165
Author(s):  
R. Saritha ◽  
N. Rajesh

The aim of this paper is to introduce and study upper and lower almost semi-I-continuous multifunctions as a generalization of upper and lower semi-I-continuous multifunctions, respectively.


2006 ◽  
Vol 80 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Donal O'Regan

AbstractNew nonoscillatory criteria are presented for second order differential inclusions. The theory relies on Ky Fan's fixed point theorem for upper semicontinuous multifunctions.


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