Geodesic
Asymptotic behavior of unbounded solutions of second-order differential equations with general nonlinearities
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 239-256 
T. A. Korchemkina. Asymptotic behavior of unbounded solutions of second-order differential equations with general nonlinearities. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 239-256. http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a10/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

One considers second-order ordinary differential equations with general nonlinearities and a bounded potential. Depending on the type of nonlinearity, qualitative behavior of solutions is described. For solutions that are unbounded near the boundaries of their domain, asymptotic formulas are obtained in the case of equations with constant or variable potentials.

[1] Kiguradze I. T., Chanturiya T. A., Asimptoticheskie svoistva reshenii neavtonomnykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1990

[2] Dulina K., Korchemkina T., “On asymptotic behavior of solutions to second-order regular and singular Emden–Fowler type differential equations with negative potential”, Int. Workshop on the Qualitative Theory of Differential Equations «QUALITDE-2016» (Tbilisi, Georgia, 2016), 71–76 | MR

[3] Evtukhov V., “On asymptotic behavior of monotonous solutions to nonlinear Emden–Fowler differential equations”, Differ. Equ., 28:6 (1992), 1076–1078 | MR | Zbl

[4] Korchemkina T., “On the behavior of solutions to second-order differential equation with general power-law nonlinearity”, Mem. Differ. Equ. Math. Phys., 73 (2018), 101–111 | MR | Zbl

[5] Astashova I., “On Kiguradze's problem on power-law asymptotic behavior of blow-up solutions to Emden–Fowler type differential equations”, Georgian Math. J., 22:2 (2017), 185–191 | MR

[6] Astashova I., “On asymptotic classification of solutions to nonlinear regular and singular third- and fourth-order differential equations with power nonlinearity”, Differential and Difference Equations with Applications, Springer Proc. Math. Statistics, Springer, New York, 2016, 185–197 | MR

[7] Astashova I., “On qualitative properties and asymptotic behavior of solutions to higher-order nonlinear differential equations”, WSEAS Trans. Math., 16:5 (2017), 39–47 | MR

[8] Jaroš J., Kusano T., “On black hole solutions of second order differential equations with a singular nonlinearity in the differential operator”, Funkc. Ekv., 43:5 (2000), 491–509 | MR | Zbl

[9] Jaroš J., Kusano T., “On white hole solutions of a class of nonlinear ordinary differential equations of the second order”, Funkc. Ekv., 45:3 (2002), 319–339 | MR | Zbl