Boundedness results of solutions to the equation $x^{\mathrm{\prime \prime \prime }}+a{x}^{\mathrm{\prime \prime }}+g(x)x^{\prime }+h(x)=p(t)$ without the hypothesis $h(x)\text{sgn}x\ge 0$$for|x|>R$.

 Access to full text

 Full (PDF)

 Full (DjVu)

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 $x^{\mathrm{\prime \prime \prime }}+a{x}^{\mathrm{\prime \prime }}+g(x)x^{\prime }+h(x)=p(t)$. «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