Geodesic
On the existence of solutions with prescribed number of zeros to regular nonlinear Emden–Fowler type third-order equation with variable coefficient
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 117-123 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A third order Emden–Fowler type equation is considered. Existence of solution with given number of zeros on given interval is proved. This theorem extends previous results, related to Emden–Fowler type equation with constant coefficient, in case of variable coefficient.
Keywords: Emden–Fowler type equation, oscillating solutions, number of zeros of solution to equation.
Mots-clés : variable coefficient 
@article{VSGU_2015_6_a15,
     author = {V. V. Rogachev},
     title = {On the existence of solutions with prescribed number of zeros to regular nonlinear {Emden{\textendash}Fowler} type third-order equation with variable coefficient},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {117--123},
     year = {2015},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_6_a15/}
}
TY  - JOUR
AU  - V. V. Rogachev
TI  - On the existence of solutions with prescribed number of zeros to regular nonlinear Emden–Fowler type third-order equation with variable coefficient
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2015
SP  - 117
EP  - 123
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VSGU_2015_6_a15/
LA  - ru
ID  - VSGU_2015_6_a15
ER  - 
%0 Journal Article
%A V. V. Rogachev
%T On the existence of solutions with prescribed number of zeros to regular nonlinear Emden–Fowler type third-order equation with variable coefficient
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2015
%P 117-123
%N 6
%U http://geodesic.mathdoc.fr/item/VSGU_2015_6_a15/
%G ru
%F VSGU_2015_6_a15
V. V. Rogachev. On the existence of solutions with prescribed number of zeros to regular nonlinear Emden–Fowler type third-order equation with variable coefficient. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 117-123. http://geodesic.mathdoc.fr/item/VSGU_2015_6_a15/

[1] Astashova I. V., “Qualitative properties of solutions to quasilinear differential equations”, Qualitative properties of solutions to differential equations and related topics of spectral analysis, scientific edition, ed. Astashova I. V., IuNITI-DANA, M., 2012, 22–288 (in Russian)

[2] Astashova I. V., Rogachev V. V., “On the number of zeros of oscillating solutions of third and fourth order equations with power nonlinearity”, Nonlinear Oscillations, 17:1 (2014), 16–31 (in Russian)

[3] Astashova I. V., Rogachev V. V., “On the existence of solutions with prescribed number of zeros to Emden–Fowler type third- and fourth-order equations”, Differential Equations, 49:11 (2013), 1509–1510 (in Russian)

[4] Kondratiev V. A., “On oscillation of solutions to linear third- and fourth-order differential equations”, Proceedings of the Academy of Sciences of the USSR, 118:1 (1958), 22–24 (in Russian) | Zbl

[5] Kondratiev V. A., “On the oscillation of solutions for third and fourth order linear differential equations”, Transactions of the Moscow Mathematical Society, 8 (1959), 259–281 (in Russian) | Zbl

[6] Kondratiev V. A., “On the oscillation of solutions for the equation $y^{(n)}+p(x)y=0$”, Transactions of the Moscow Mathematical Society, 10 (1961), 419–436 (in Russian) | Zbl

[7] Kiguradze I. T., Chanturia T. A., Asymptotic properties of solutions of nonautonomous ordinary differential equations, Nauka, M., 1990, 432 pp. (in Russian)

[8] Smirnov S., “On Some Spectral Properties of Third Order Nonlinear Boundary Value Problems”, Mathematical Modelling and Analysis, 17:1 (2012), 78–89 (in Russian) | DOI | MR | Zbl