Geodesic
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. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 80 (1986) no. 7-12, pp. 533-539 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

Voir la notice de l'article

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi $h (x) \, \text{sgn} x \ge 0$$for |x| > R$, si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta. 
@article{RLINA_1986_8_80_7-12_a6,
     author = {Andres, J\'an},
     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. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
     pages = {533--539},
     year = {1986},
     volume = {Ser. 8, 80},
     number = {7-12},
     zbl = {0722.34027},
     mrnumber = {0976947},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLINA_1986_8_80_7-12_a6/}
}
TY  - JOUR
AU  - Andres, Ján
TI  - 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 $|x| > R$.
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali
PY  - 1986
SP  - 533
EP  - 539
VL  - 80
IS  - 7-12
UR  - http://geodesic.mathdoc.fr/item/RLINA_1986_8_80_7-12_a6/
LA  - en
ID  - RLINA_1986_8_80_7-12_a6
ER  - 
%0 Journal Article
%A Andres, Ján
%T 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 $|x| > R$.
%J Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali
%D 1986
%P 533-539
%V 80
%N 7-12
%U http://geodesic.mathdoc.fr/item/RLINA_1986_8_80_7-12_a6/
%G en
%F RLINA_1986_8_80_7-12_a6
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. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 80 (1986) no. 7-12, pp. 533-539. http://geodesic.mathdoc.fr/item/RLINA_1986_8_80_7-12_a6/

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

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

[3] J.O.C. Ezeilo (1968) - On the boundedness of solutions of the equation $x^{\prime\prime\prime} + ax^{\prime\prime}+ g (x) x^{\prime}+ h (x) = p (t)$. «Ann. Mat. Pura Appl.», 4, 80, 281-299. | MR | Zbl

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

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

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

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

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

[9] J. Andres (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. | fulltext EuDML | MR | Zbl

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

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

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

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

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