Boundedness results of solutions to the equation x′′′+a⁢x′′+g⁢(x)⁢x′+h⁢(x)=p⁢(t) without the hypothesis h⁢(x)⁢sgn⁡x≥0 for |x|>R.
Andres, Ján
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 80 (1986), p. 533-539 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h⁢(x)⁢sgn⁢x≥0f⁢o⁢r⁢|x|>R, si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.

Publié le : 1986-12-01
@article{RLINA_1986_8_80_7-12_533_0,
     author = {J\'an Andres},
     title = {Boundedness results of solutions to the equation $x^{\prime\prime\prime} + ax^{\prime\prime}+ g (x) x^{\prime}+ h (x) = p (t)$ without the hypothesis $h (x) \, \operatorname{sgn} x \ge 0$ for $|x| > R$.},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {80},
     year = {1986},
     pages = {533-539},
     zbl = {0722.34027},
     mrnumber = {0976947},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1986_8_80_7-12_533_0}
}

Andres, Ján. Boundedness results of solutions to the equation $x^{\prime\prime\prime} + ax^{\prime\prime}+ g (x) x^{\prime}+ h (x) = p (t)$ without the hypothesis $h (x) \, \operatorname{sgn} x \ge 0$ for $|x| > R$.. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 80 (1986) pp. 533-539. http://gdmltest.u-ga.fr/item/RLINA_1986_8_80_7-12_533_0/

[1] Reissig, R., Sansone, G. and Conti, R. (1969) - Nichtlineare Dijferentialgleichungen höherer Ordnung. Cremonese, Roma. | MR 241749 | Zbl 0172.10801

[2] Ezeilo, J.O.C. and Tejumola, H.O. (1973) - Boundedness theorems for certain third order equations. «Atti Accad. Naz. Lincei», (8), 55, 194-201. | MR 364784 | Zbl 0295.34022

[3] Ezeilo, J.O.C. (1968) - On the boundedness of solutions of the equation x′′′+a⁢x′′+g⁢(x)⁢x′+h⁢(x)=p⁢(t). «Ann. Mat. Pura Appl.», 4, 80, 281-299. | MR 241753 | Zbl 0211.40102

[4] Swick, K.E. (1974) - Boundedness and stability for nonlinear third order differential equations. «Atti Accad. Naz. Lincei», (8), 56, 859-865. | MR 399597 | Zbl 0326.34062

[5] Swick, K.E. (1970) - Asymptotic behavior of the solutions of certain third order differential equations. «SIAM J. Appl. Math.», 19, 96-102. | MR 267212 | Zbl 0212.11403

[6] Voráček, J. (1966) - Einige Bemerkungen über eine nichtlineare Differentialgleichungen dritten Ordnung. «Arch. Math.», 2, 19-26. | MR 199501 | Zbl 0244.34023

[7] Voráček, J. (1970) - Über eine nichtlineare Differentialgleichung dritter Ordnung. «Czech. Math. J.», 20, 207-219. | MR 259237 | Zbl 0201.11602

[8] Andres, J. (1986) - Boundedness of solutions of the third order differential equation with the oscillatory restoring and forcing terms. «Czech. Math. J.», 1, 1-6. | MR 822859 | Zbl 0608.34039

[9] Andres, J. (1986) - On stability and instability of the roots of the oscillatory function in a certain nonlinear differential equation of the third order. «Čas. pěst. mat.», 3, 225-229. | MR 853786 | Zbl 0609.34058

[10] Reissig, R. (1973/74) - Phasenraum-Methoden zum Studium nichtlinearerer Dijferentialgleichungen. «Jber. Deutch. Math.-Verein», 75 (3), 1, 130-139. | MR 477300 | Zbl 0287.34053

[11] Krasnosel'Ski, M.A. (1966) - Translation operator along the trajectories of differential equations. «Nauka, Moscow» (in Russian).

[12] Yoshizawa, T. (1966) - Stability theory by Liapunov's second method. «Math. Soc. Japan», Tokyo. | MR 208086 | Zbl 0144.10802

[13] Andres, J. - Dichotomies for solutions of a certain third order nonlinear differential equation which is not from the class D. To appear in «Fasc. Math.». | MR 942320 | Zbl 0645.34048

[14] Anderson, L.R. (1970) - Integral manifolds of a class of third order autonomous differential equations. «J. Diff. Eqs.», 7, 274-286. | MR 254319 | Zbl 0215.15005