A Note on the Solutions of a Sturm-Liouville Differential Inclusion with "Maxima"

Document Type: Original Article

Author

1-Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, 010014 Bucharest, Romania. 2-Academy of Romanian Scientists, Splaiul Independentei 54, 050094 Bucharest, Romania.

Abstract

We consider a boundary value problem associated with a Sturm-Liouville differential inclusion with "maxima" and we prove a Filippov type existence result for this problem.

Keywords


[1] J.P. Aubin, H. Frankowska, Set-valued Analysis, Birkhauser, Basel, (1990).


[2] D.D. Bainov, S. Hristova, Differential equations with maxima, Chapman and Hall/CRC, Boca Raton, (2011).


[3] A. Cernea, Existence of solutions for a class of functional differential inclusions with "maxima", Fixed Point
Theory, 19 (2018), 503-514.


[4] A. Cernea, On a Sturm-Liouville type functional differential inclusion with "maxima", Adv. Dyn. Syst. Appl., 13
(2018), 101-112.


[5] A.F. Filippov, Classical solutions of differential equations with multivalued right-hand side, SIAM J. Control, 5
(1967), 609-621.


[6] L. Georgiev, V.G. Angelov, On the existence and uniqueness of solutions for maximum equations, Glasnik Mat.,
37 (2002), 275-281.


[7] P. Gonzalez, M. Pinto, Convergent solutions of certain nonlinear differential equations with maxima, Math.
Comput. Modelling, 45 (2007), 1-10.


[8] E.N. Mahmudov, Optimization of Mayer problem with Sturm-Liouville type differential inclusion, J. Optim.
Theory Appl., 177 (2018), 345-375.


[9] M. Malgorzata, G. Zhang, On unstable neutral difference equations with "maxima", Math. Slovaca, 56 (2006),
451-463.


[10] D. Otrocol, Systems of functional differential equations with maxima, of mixed type, Electronic J. Qual. Theory
Diff. Equations, 2014 (2014), 9 pages.


[11] D. Otrocol, I.A. Rus, Functional-differential equations with "maxima" via weakly Picard operator theory, Bull.
Math. Soc. Sci. Math. Roumanie, 51(99) (2008), 253-261.


[12] D. Otrocol, I.A. Rus, Functional-differential equations with "maxima" of mixed type, Fixed Point Theory, 9
(2008), 207-220.


[13] E. P. Popov, Automatic regulation and control, Nauka, Moskow, (1966) (in Russian).