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 f o r | x | > R .

Ján Andres

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1986)

  • Volume: 80, Issue: 7-12, page 533-539
  • ISSN: 1120-6330

How to cite

top

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) \, \text{sgn} x \ge 0$$for |x| > R$.." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 80.7-12 (1986): 533-539. <http://eudml.org/doc/287214>.

@article{Andres1986,
author = {Andres, Ján},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Lyapunov functions; bounded solution},
language = {eng},
month = {12},
number = {7-12},
pages = {533-539},
publisher = {Accademia Nazionale dei Lincei},
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) \, \text\{sgn\} x \ge 0$$for |x| > R$.},
url = {http://eudml.org/doc/287214},
volume = {80},
year = {1986},
}

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) \, \text{sgn} x \ge 0$$for |x| > R$.
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1986/12//
PB - Accademia Nazionale dei Lincei
VL - 80
IS - 7-12
SP - 533
EP - 539
LA - eng
KW - Lyapunov functions; bounded solution
UR - http://eudml.org/doc/287214
ER -

References

top
  1. REISSIG, R., SANSONE, G. and CONTI, R. (1969) - Nichtlineare Dijferentialgleichungen höherer Ordnung. Cremonese, Roma. Zbl0172.10801MR241749
  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. Zbl0295.34022MR364784
  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. Zbl0211.40102MR241753
  4. SWICK, K.E. (1974) - Boundedness and stability for nonlinear third order differential equations. «Atti Accad. Naz. Lincei», (8), 56, 859-865. Zbl0326.34062MR399597
  5. SWICK, K.E. (1970) - Asymptotic behavior of the solutions of certain third order differential equations. «SIAM J. Appl. Math.», 19, 96-102. Zbl0212.11403MR267212
  6. VORÁČEK, J. (1966) - Einige Bemerkungen über eine nichtlineare Differentialgleichungen dritten Ordnung. «Arch. Math.», 2, 19-26. Zbl0244.34023MR199501
  7. VORÁČEK, J. (1970) - Über eine nichtlineare Differentialgleichung dritter Ordnung. «Czech. Math. J.», 20, 207-219. Zbl0201.11602MR259237
  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. Zbl0608.34039MR822859
  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. Zbl0609.34058MR853786
  10. REISSIG, R. (1973/74) - Phasenraum-Methoden zum Studium nichtlinearerer Dijferentialgleichungen. «Jber. Deutch. Math.-Verein», 75 (3), 1, 130-139. Zbl0287.34053MR477300
  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. Zbl0144.10802MR208086
  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.». Zbl0645.34048MR942320
  14. ANDERSON, L.R. (1970) - Integral manifolds of a class of third order autonomous differential equations. «J. Diff. Eqs.», 7, 274-286. Zbl0215.15005MR254319

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.