Electron. J. Diff. Equ., Vol. 2015 (2015), No. 107, pp. 1-13.

Measure integral inclusions with fast oscillating data

Bianca-Renata Satco

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.

Submitted April 29, 2014. Published April 21, 2015.
Math Subject Classifications: 34A60, 93C30, 26A42, 26A39.
Key Words: Measure integral inclusion; Kurzweil-Stieltjes integral; regulated function; bounded variation.

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Bianca-Renata Satco
Stefan cel Mare University
Faculty of Electrical Engineering and Computer Science
Universitatii 13 - 720229 Suceava, Romania
email: bianca.satco@eed.usv.ro Phone/Fax: +40 230 524 801

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