We prove the existence of regulated or bounded variation solutions, via a nonlinear alternative of Leray-Schauder type, for the measure integral inclusion
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
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