Existence and uniqueness of a positive solution to a boundary value problem for a second order functional-differential equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 3-8.

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

In the paper, a boundary value problem for one functional-differential equation of the second order with sufficiently general linear homogeneous boundary conditions. On the basis of the theory of semi-ordered spaces with the help of special topological means, the existence of a unique positive solution to the problem under study is proved.
Mots-clés : positive solution
Keywords: boundary value problem, cone, asymptotic derivative, spectral radius.
@article{IVM_2021_12_a0,
     author = {G. E. Abduragimov},
     title = {Existence and uniqueness of a positive solution to a boundary value problem for a second order functional-differential equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--8},
     publisher = {mathdoc},
     number = {12},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_12_a0/}
}
TY  - JOUR
AU  - G. E. Abduragimov
TI  - Existence and uniqueness of a positive solution to a boundary value problem for a second order functional-differential equation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 3
EP  - 8
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_12_a0/
LA  - ru
ID  - IVM_2021_12_a0
ER  - 
%0 Journal Article
%A G. E. Abduragimov
%T Existence and uniqueness of a positive solution to a boundary value problem for a second order functional-differential equation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 3-8
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_12_a0/
%G ru
%F IVM_2021_12_a0
G. E. Abduragimov. Existence and uniqueness of a positive solution to a boundary value problem for a second order functional-differential equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 3-8. http://geodesic.mathdoc.fr/item/IVM_2021_12_a0/

[1] Azbelev N. V., Maksimov V. P., Simonov P. M., “Funktsionalno-differentsialnye uravneniya i ikh prilozheniya”, Vestn. Udmurtsk. gos. un-ta. Ser. Matem., 1 (2009), 3–23

[2] Wong F. H., Wang S. P., Chen T. G., “Existence of positive solutions for second order functional differential equations”, Comput. and Math. Appl., 56:10 (2008), 2580–2587 | DOI | Zbl

[3] Ma R., “Positive solutions for boundary value problems of functional differential equations”, Appl. Math. Comput., 193:1 (2007), 66–72 | Zbl

[4] Zima M., “On positive solutions of functional-differential equations in banach spaces”, J. Inequalities and Appl., 6:3 (2000), 359–371

[5] Agarwal R. P., Stanek S., “Positive solutions of singular value problems for delay differential equations”, Dyn. Syst. Appl., 16:4 (2007), 755–770 | Zbl

[6] Hong C., Yeh C., Lee C., Wong F., “Existence of positive solutions for functional equations”, Comp. and Math. Appl., 40:6–7 (2000), 783–792 | DOI | Zbl

[7] Sun Y., Han M. M., Debnath L., “Existence of positive periodic solutions for a class of functional differential equations”, Appl. Math. and Comput., 190:1 (2007), 699–704 | Zbl

[8] Weng P., Jiang D., “Existence of positive solutions for boundary value problem of second-order FDE”, Comput. and Math. Appl., 37:10 (1999), 1–9 | DOI | Zbl

[9] Hong C., Yeh C., Lee C., Wong F., “Existence of positive solutions for higher-order functional differential equations”, J. Math. Anal. Appl., 297:1 (2004), 14–23 | DOI | Zbl

[10] Yin F., Fugi F., Li Y., “The existence of positive solutions for the quasilinear functional delay differential equations”, J. Math. Study, 35:4 (2002), 364–370 | Zbl

[11] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatgiz, M., 1962

[12] Abduragimov G. E., “O polozhitelnykh resheniyakh kraevoi zadachi dlya odnogo nelineinogo-funktsionalno differentsialnogo uravneniya $2$-go poryadka”, Vestn. Dagestansk. gos. un-ta. Estestv. nauki, IV (1997), 121–123

[13] Krein S. G., Funktsionalnyi analiz, Nauka, M., 1972

[14] Zabreiko P. P., Krasnoselskii M. A., Stetsenko V. Ya., “Ob otsenkakh spektralnogo radiusa lineinykh polozhitelnykh operatoro”, Matem. zametki, 1:4 (1967), 461–470