On positive periodic solutions of first order functional differential equations
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 21-28.

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

The periodic boundary value problem for linear functional differential equations is considered. In the case when the Green function changes its sign, conditions for the positiveness of solutions are obtained.
Keywords: functional differential equations, periodic boundary value problem, resonance
Mots-clés : positive solutions.
@article{IIMI_2015_46_2_a2,
     author = {E. I. Bravyi},
     title = {On positive periodic solutions of first order functional differential equations},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {21--28},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a2/}
}
TY  - JOUR
AU  - E. I. Bravyi
TI  - On positive periodic solutions of first order functional differential equations
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2015
SP  - 21
EP  - 28
VL  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a2/
LA  - ru
ID  - IIMI_2015_46_2_a2
ER  - 
%0 Journal Article
%A E. I. Bravyi
%T On positive periodic solutions of first order functional differential equations
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2015
%P 21-28
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a2/
%G ru
%F IIMI_2015_46_2_a2
E. I. Bravyi. On positive periodic solutions of first order functional differential equations. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 21-28. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a2/

[1] Liz E., Nieto J. J., “Periodic boundary value problems for a class of functional differential equations”, Journal of Mathematical Analysis and Applications, 200:3 (1996), 680–686 | DOI | MR | Zbl

[2] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Introduction to the theory of functional differential equations, Nauka, M., 1991

[3] Jiang D., Wei J., “Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations”, Nonlinear Analysis: Theory, Methods Applications, 50:7 (2002), 885–898 | DOI | MR | Zbl

[4] Jiang D., Nieto J. J., Zuo W., “On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations”, Journal of Mathematical Analysis and Applications, 289:2 (2004), 691–699 | DOI | MR | Zbl

[5] Nieto J. J., Rodríguez-López R., “Monotone method for first-order functional differential equations”, Computers and Mathematics with Applications, 52:3–4 (2006), 471–484 | DOI | MR | Zbl

[6] Wong F. H., Wang S. P., Chen T. G., “Existence of positive solutions for second order functional differential equations”, Computers and Mathematics with Applications, 56:10 (2008), 2580–2587 | DOI | MR | Zbl

[7] Domoshnitsky A., Hakl R., Šremr J., “Component-wise positivity of solutions to periodic boundary problem for linear functional differential system”, Journal of Inequalities and Applications, 2012 (2012) | DOI | MR

[8] Agarwal R. P., Berezansky L., Braverman E., Domoshnitsky A., Nonoscillation theory of functional differential equations with applications, Springer, New York, 2012, XVI+520 pp. | MR | Zbl

[9] Ma R., Lu Y., “Existence of positive periodic solutions for second-order functional differential equations”, Monatshefte fur Mathematik, 17:1 (2014), 67–81 | MR

[10] Calamai A., Infante G., “Nontrivial solutions of boundary value problems for second-order functional differential equations”, Annali di Matematica Pura ed Applicata, 2015 | DOI

[11] Krasnosel'skii M. A., Lifshits E. A., Sobolev A. V., Positive linear systems, Nauka, M., 1985

[12] Lomtatidze A. G., Hakl R., Půža B., “On the periodic boundary value problem for first-order functional-differential equations”, Differential Equations, 39:3 (2003), 344–352 | DOI | MR | Zbl

[13] Bravyi E., “On estimates of solutions of the periodic boundary value problem for first-order functional differential equations”, Boundary Value Problems, 2014 (2014) | DOI | MR