Geodesic
Existence results for second-order nonlinear differential inclusion with nonlocal boundary conditions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 1, pp. 35-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we investigate the existence of solutions for a second-order differential inclusion with nonlocal boundary conditions. To establish the existence results for the given problem, first we apply Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo. Second, our result is based on the fixed point theorem for multivalued maps due to Covitz and Nadler. An example is given to illustrate the obtained results. 
@article{SJVM_2021_24_1_a3,
     author = {N. Bouteraa and S. Benaicha},
     title = {Existence results for second-order nonlinear differential inclusion with nonlocal boundary conditions},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {35--45},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a3/}
}
TY  - JOUR
AU  - N. Bouteraa
AU  - S. Benaicha
TI  - Existence results for second-order nonlinear differential inclusion with nonlocal boundary conditions
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2021
SP  - 35
EP  - 45
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a3/
LA  - ru
ID  - SJVM_2021_24_1_a3
ER  - 
%0 Journal Article
%A N. Bouteraa
%A S. Benaicha
%T Existence results for second-order nonlinear differential inclusion with nonlocal boundary conditions
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2021
%P 35-45
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a3/
%G ru
%F SJVM_2021_24_1_a3
N. Bouteraa; S. Benaicha. Existence results for second-order nonlinear differential inclusion with nonlocal boundary conditions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 1, pp. 35-45. http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a3/

[1] A. Ashyralyev, O. Yildirim, “On multipoint nonlocal boundary value problems for hyperbolic differential and difference equations”, Taiwanese Journal of Mathematics, 14 (2010), 165–194 | DOI | MR | Zbl

[2] A. Ashyralyev, E. Ozturk, “On Bitsadze-Samarskii type nonlocal boundary value problems for elliptic differential and difference equations: Well-posedness”, Applied Mathematics and Computation, 219 (2012), 1093–1107 | DOI | MR | Zbl

[3] J. P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, 2012 | MR

[4] A. V. Bitsadze, A. A. Samarskii, “On some simple generalizations of linear elliptic boundary problems”, Dokl. Akad. Nauk SSSR, 185:4 (1969), 739–740 | MR | Zbl

[5] A. Bressan, G. Colombo, “Extensions and selections of maps with decomposable values”, Studia Mathematica, 90:1 (1988), 69–86 | DOI | MR | Zbl

[6] A. Bressan, Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem, Oxford University Press, London, 2000 | MR | Zbl

[7] N. Bouteraa, S. Benaicha, “Triple positive solutions of higher-order nonlinear boundary value problems”, J. Comput. Sci. Comp. Math., 7:2 (2017), 25–31 | DOI | MR

[8] N. Bouteraa, S. Benaicha, “Existence of solution for third-order three-point boundary value problem”, Mathematica, 60(83):1 (2018), 21–31 | DOI | MR | Zbl

[9] N. Bouteraa, S. Benaicha, “Existence of solutions for nonlocal boundary value problem for Caputo nonlinear fractional differential inclusion”, J. of Mathematical Sciences and Modelling, 1:1 (2018), 45–55 | DOI | MR

[10] N. Bouteraa, S. Benaicha, “Positive periodic solutions for a class of fourth-order nonlinear differential equations”, Numerical Analysis and Applications, 12:1 (2019), 1–14 | DOI | MR

[11] N. Bouteraa, S. Benaicha, “Existence results for fractional differential inclusion with nonlocal boundary conditions”, Rivista di Matematica della Universita di Parma (to appear) | MR

[12] H. Covitz, S. B. Nadler, “Multi-valued contraction mappings in generalized metric spaces”, Israel J. Math., 8 (1970), 5–11 | DOI | MR | Zbl

[13] C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, Springer, Berlin, 1977 | DOI | MR | Zbl

[14] K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin–New-York, 1982 | MR

[15] M. Frigon, A. Granas, “Theoremes d'existence pour des inclusions differentielles sans convexit”, C. R. Acad. Sci. Paris. Ser. I, 310 (1990), 819–822 | MR | Zbl

[16] L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and Its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999 | MR | Zbl

[17] S. Hu, N. Papageorgiou, Handbook of Multivalued Analysis, v. I, Theory, Kluwer Academic Publishers, Dordrecht–Boston–London, 1977 | MR

[18] V. A. Il'in, E. I. Moiseev, “Second kind nonlocal boundary value problem for Sturm-Liouville operator in differential and difference treatement”, Differential Equations, 23:7 (1987), 1198–1207

[19] V. A. Il'in, E. I. Moiseev, “An a priori estimate for the solution of a problem associated with a nonlocal boundary value problem of the first kind”, Differential Equations, 24:5 (1988), 519–526 | MR | Zbl

[20] M. Kisielewicz, Differential Inclusions and Optimal Control, Mathematics and its Applications (East European Series), 44, Kluwer Academic Publishers, Dordrecht, the Netherlands, 1991 | MR | Zbl

[21] R. von Mises, “Beitrag zum Oszillationsproblem”, Festschrift H. Weber, Leipzig–Berlin, 1912, 252–282 | Zbl

[22] M. Picone, “Sui valori eccezionali di un parametro da cui dipende un'equzione differenziale lineare del second'ordine”, Ann. Scuola Norm. Sup. Pisa, 11 (1910), 1–14 | MR

[23] A. Rezaiguia, S. Kelaiaia, “Existence results for third-order differential inclusion with threepoint boundary value problems”, Acta Math. Univ. Comenianae, 2 (2016), 311–318 | MR | Zbl

[24] A. Sommerfeld, “Ein Beitrag zur hydrodynamishen Erklaerung der turbulenten Fluessigkeitsbewegungen”, Proc. of the 4th International Congress of Mathematicians, v. III, 116–124 | Zbl

[25] D. R. Smart, Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1977 | MR