Geodesic
Measure integral inclusions with fast oscillating data
Electronic journal of differential equations, Tome 2015 (2015)
We prove the existence of regulated or bounded variation solutions, via a nonlinear alternative of Leray-Schauder type, for the measure integral inclusion

$ x(t) \in \int_0^t F(s, x(s)) \,du(s), $

under the assumptions of regularity, respectively bounded variation, on the function u. Our approach is based on the properties of Kurzweil-Stieltjes integral that, unlike the classical integrals, can be used for fast oscillating multifunctions on the right hand side and the results allow one to study (by taking the function u of a particular form) continuous or discrete problems, as well as impulsive or retarded problems.
Classification : 34A60, 93C30, 26A42, 26A39
Keywords: measure integral inclusion, kurzweil-Stieltjes integral, regulated function, bounded variation 
@article{EJDE_2015__2015__a72,
     author = {Satco,  Bianca-Renata},
     title = {Measure integral inclusions with fast oscillating data},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1314.45005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a72/}
}
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Satco,  Bianca-Renata. Measure integral inclusions with fast oscillating data. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a72/