On Fucik Spectra and Periodic Solutions
Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 910-922.

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

In this paper, we continue extending the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand side. To this end, we construct a new version of the method of shifts along trajectories. We compare the results obtained by the new approach and those obtained by the method of Fucik spectra.
@article{MZM_2003_73_6_a12,
     author = {V. V. Filippov},
     title = {On {Fucik} {Spectra} and {Periodic} {Solutions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {910--922},
     publisher = {mathdoc},
     volume = {73},
     number = {6},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a12/}
}
TY  - JOUR
AU  - V. V. Filippov
TI  - On Fucik Spectra and Periodic Solutions
JO  - Matematičeskie zametki
PY  - 2003
SP  - 910
EP  - 922
VL  - 73
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a12/
LA  - ru
ID  - MZM_2003_73_6_a12
ER  - 
%0 Journal Article
%A V. V. Filippov
%T On Fucik Spectra and Periodic Solutions
%J Matematičeskie zametki
%D 2003
%P 910-922
%V 73
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a12/
%G ru
%F MZM_2003_73_6_a12
V. V. Filippov. On Fucik Spectra and Periodic Solutions. Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 910-922. http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a12/

[1] Filippov V. V., “O gomologicheskikh svoistvakh mnozhestv reshenii obyknovennykh differentsialnykh uravnenii”, Matem. sb., 188:6 (1997), 139–160 | MR | Zbl

[2] Filippov V. V., “Smes metodov Lere–Shaudera i Puankare–Andronova v zadache o periodicheskikh resheniyakh obyknovennykh differentsialnykh uravnenii”, Differents. uravneniya, 35:12 (1999), 1709–1711 | MR | Zbl

[3] Filippov V. V., “Remarks on periodic solutions of ordinary differential equations”, J. Dynamical and Control Systems, 6:3 (2000), 431–451 | DOI | MR | Zbl

[4] Gossez J.-P., Omari P., “Nonresonance with respect to the Fučik spectrum for periodic solutions of second order ordinary differential equations”, Nonlinear Anal. Th. Methods Appl., 14 (1990), 1079–1104 | DOI | MR

[5] Gossez J.-P., Omari P., “Periodic solutions of a second order ordinary differential equation: a necessary and sufficient condition for nonresonance”, J. of Differential Equations, 94:1 (1991), 67–82 | DOI | MR | Zbl

[6] Habets P., Omari P., Zanolin F., “Nonresonance conditions on the potential with respect to the Fučik spectrum for the boundary value problem”, Rocky Mountain J. Math., 25:4 (1995), 1305–1340 | DOI | MR | Zbl

[7] Mawhin J., “Continuation theorems and periodic solutions of ordinary differential equations”, Topological Methods in Differential Equations and Inclusions, Kluwer Academic Publishers, Dordrecht–Boston–London, 1995, 291–376 | MR

[8] Gabdrakhmanov S. R., “Prostranstva reshenii i spektr Fuchika”, Differents. uravneniya, 39:3, 298–298 | MR | Zbl

[9] Filippov V. V., “Topologicheskoe stroenie prostranstv reshenii obyknovennykh differentsialnykh uravnenii”, UMN, 48:1 (1993), 103–154 | MR | Zbl

[10] Filippov V. V., Prostranstva reshenii obyknovennykh differentsialnykh uravnenii, Izd-vo MGU, M., 1993 | Zbl

[11] Filippov V. V., “Basic topological structures of the theory of ordinary differential equations”, Topology in Nonlinear Analysis, Banach Center Publications, 35, Warsaw, 1996, 171–192 | Zbl

[12] Filippov V. V., Basic Topological Structures of Ordinary Differential Equations, Kluwer Academic Publishers, Dordrecht–Boston–London, 1998 | Zbl

[13] Filippov V. V., “O differentsialnykh vklyucheniyakh vtorogo poryadka”, Fundamentalnaya i prikladnaya matem., 3:2 (1997), 587–623 | MR | Zbl

[14] Filippov V. V., “O suschestvovanii periodicheskikh reshenii”, Matem. zametki, 61:5 (1997), 769–784 | MR | Zbl

[15] Filippov V. V., “O teoreme edinstvennosti resheniya zadachi Koshi dlya obyknovennogo differentsialnogo uravneniya”, Differents. uravneniya, 30:6 (1994), 1005–1009 | MR | Zbl