Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations
A. T. ADEMOLA; M. O. OGUNDIRAN; P. O. ARAWOMO
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2015)
- Volume: 54, Issue: 1, page 5-18
- ISSN: 0231-9721
Access Full Article
topAbstract
topHow to cite
topADEMOLA, A. T., OGUNDIRAN, M. O., and ARAWOMO, P. O.. "Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 54.1 (2015): 5-18. <http://eudml.org/doc/271596>.
@article{ADEMOLA2015,
abstract = {In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.},
author = {ADEMOLA, A. T., OGUNDIRAN, M. O., ARAWOMO, P. O.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Third order; nonlinear differential equation; uniform stability; uniform ultimate boundedness; periodic solutions},
language = {eng},
number = {1},
pages = {5-18},
publisher = {Palacký University Olomouc},
title = {Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations},
url = {http://eudml.org/doc/271596},
volume = {54},
year = {2015},
}
TY - JOUR
AU - ADEMOLA, A. T.
AU - OGUNDIRAN, M. O.
AU - ARAWOMO, P. O.
TI - Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2015
PB - Palacký University Olomouc
VL - 54
IS - 1
SP - 5
EP - 18
AB - In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.
LA - eng
KW - Third order; nonlinear differential equation; uniform stability; uniform ultimate boundedness; periodic solutions
UR - http://eudml.org/doc/271596
ER -
References
top- Ademola, A. T., Arawomo, P. O., On the asymptotic behaviour of solutions of certain differential equations of the third order, Proyecciones Journal of Mathematics 33, 1 (2014), 111–132. (2014) Zbl1302.34076MR3162791
- Ademola, A. T., Arawomo, P. O., Generalization of some qualitative behaviour of solutions of third order nonlinear differential equations, Differential Equations and Control Processes N 1 (2012), 97–113. (2012) MR2977146
- Ademola, A. T., Arawomo, P. O., Asymptotic behaviour of solutions of third order nonlinear differential equations, Acta Univ. Sapientiae, Mathematica 3, 2 (2011), 197–211. (2011) Zbl1260.34100MR2915835
- Ademola, A. T., Arawomo, P. O., 10.1007/s13370-011-0034-x, Afr. Mat. 23 (2012), 261–271. (2012) Zbl1266.34051MR2958973DOI10.1007/s13370-011-0034-x
- Ademola, A. T., Arawomo, P. O., Boundedness and stability of solutions of some nonlinear differential equations of the third-order, The Pacific Journal of Science and Technology 10, 2 (2009), 187–193. (2009) MR2881138
- Ademola, A. T., Arawomo, P. O., Stability and ultimate boundedness of solutions to certain third-order differential equations, Applied Mathematics E-Notes 10 (2010), 61–69. (2010) Zbl1194.34103MR2606838
- Ademola, A. T., Arawomo, P. O., Stability and uniform ultimate boundedness of solutions of a third-order differential equation, International Journal of Applied Mathematics 23, 1 (2010), 11–22. (2010) Zbl1201.34054MR2643291
- Ademola, A. T., Arawomo, P. O., Stability and uniform ultimate boundedness of solutions of some third order differential equations, Acta Mathematica Academiae Paedagogicae Nyíregyháziensis 27 (2011), 51–59. (2011) Zbl1240.34259MR2813591
- Ademola, A. T., Arawomo, P. O., Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order, Kragujevac J. Math. 35, 3 (2011), 431–445. (2011) Zbl1265.34191MR2881138
- Ademola, A. T., Ogundiran, M. O., Arawomo, P. O., Adesina, O. A., 10.1016/j.amc.2010.04.022, Appl. Math. Comput. 216 (2010), 3044–3049. (2010) MR2653118DOI10.1016/j.amc.2010.04.022
- Afuwape, A. U., Adesina, O. A., On the bounds for mean-values of solutions to certain third-order nonlinear differential equations, Fasciculi Mathematici 36 (2005), 5–14. (2005) Zbl1127.34019MR2223637
- Andres, J., Boundedness results for solutions of the equation without the hypothesis for , Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 80, 8 (1986), 533–539. (1986) MR0976947
- Antoisewicz, H. A., 10.1112/jlms/s1-30.1.64, J. London Math. Soc. 30 (1955), 64–67. (1955) DOI10.1112/jlms/s1-30.1.64
- Babaev, E. V., Hefferlin, R., Concept of chemical periodicity: from Mendeleev Table to Molecular Hyper-periodicity patterns, In: Research Studies Press, London, 1996, 24–81. (1996)
- Bereketoǧlu, H., Györi, I., On the boundedness of solutions of a third-order nonlinear differential equation, Dynam. Systems Appl. 6, 2 (1997), 263–270. (1997) MR1461442
- Callahan, J., Cox, D., Hoffman, K., O’Shea, D., Pollatsek, H., Senechal, L., L., Calculus in Context, The Five College Calculus Project, Five Colleges, 2008. (2008)
- Chukwu, E. N., 10.1007/BF02417013, Ann. Mat. Pura. Appl. 104, 4 (1975), 123–149. (1975) MR0377180DOI10.1007/BF02417013
- Ezeilo, J. O. C., 10.1112/jlms/s1-36.1.439, J. London Math. Soc. 36 (1961), 439–444. (1961) Zbl0104.06501MR0136820DOI10.1112/jlms/s1-36.1.439
- Ezeilo, J. O. C., 10.1112/jlms/s1-38.1.11, J. London Math. Soc. 38 (1963), 11–16. (1963) Zbl0116.06902MR0166450DOI10.1112/jlms/s1-38.1.11
- Ezeilo, J. O. C., A boundedness theorem for a certain third-order differential equation, Proc. London Math. Soc. 13, 3 (1963), 99–124. (1963) Zbl0116.06902MR0142850
- Hara, T., 10.1016/0022-247X(81)90122-0, J. Math. Anal. Appl. 80, 2 (1981), 533–544. (1981) MR0614848DOI10.1016/0022-247X(81)90122-0
- Mehri, B., Niksirat, M. A., 10.1016/j.cam.2004.04.011, J. Comp. & Appl. Math. 174 (2005), 239–249. (2005) Zbl1069.34064MR2106439DOI10.1016/j.cam.2004.04.011
- Mehri, B., Shadman, D., Boundedness of solutions of certain third-order differential equation, Math. Inequal. Appl., 4 (1999), 545–549. (1999) Zbl0943.34022MR1717047
- Mehri, B., Shadman, D., On the existence of periodic solutions of a certain class of second order nonlinear differential equation, Math. Inequal. Appl. 1, 3 (1998), 431–436. (1998) MR1629412
- Mehri, B., Shadman, D., Periodic solutions of a certain non-linear third order differential equation, Scientia Iranica 11 (2004), 181–184. (2004) MR2106566
- Mehri, B., Periodic solution for certain non linear third-order differential equation, Indian J. Pure Appl. Math. 21, 3 (1990), 203–210. (1990) Zbl0708.34030MR1044260
- Minhós, F., Periodic solutions for a third order differential equation under conditions on the potential, Portugaliae Mathematica 55, 4 (1998), 475–484. (1998) Zbl0923.34045MR1672255
- LaSalle, J., Lefschetz, S., Stability by Liapunov’s direct method with applications, Academic Press, New York–London, 1961. (1961) MR0132876
- Ogundare, B. S., On the boundedness and stability results for the solutions of certain third-order nonlinear differential equations, Kragujevac J. Math. 29 (2006), 37–48. (2006) MR2288487
- Omeike, M. O., New result in the ultimate boundedness of solutions of a third-order nonlinear ordinary differential equation, J. Inequal. Pure and Appl. Math. 9, 1 (2008), Art. 15, 1–8. (2008) Zbl1173.34321MR2391282
- Reissig, R., Sansone, G., Conti, R., Nonlinear Differential Equations of Higher Order, Noordhoff International Publishing, Leyeden, 1974. (1974) MR0344556
- Rouche, N., Habets, N., Laloy, M., Stability Theory by Liapunov’s Direct Method, Applied Mathematical Sciences 22, Spriger-Verlag, New York–Heidelberg–Berlin, 1977. (1977) Zbl0364.34022MR0450715
- Shadman, D., Mehri, B., 10.1002/zamm.19950750218, Z Angew. Math. Mech. 75, 2 (1995), 164–166. (1995) Zbl0828.34029MR1319334DOI10.1002/zamm.19950750218
- Swick, K. E., 10.1112/jlms/s1-44.1.347, J. London Math. Soc. 44 (1969), 347–359. (1969) MR0236482DOI10.1112/jlms/s1-44.1.347
- Tejumola, H. O., A note on the boundedness of solutions of some nonlinear differential equations of the third-order, Ghana J. of Science 11, 2 (1970), 117–118. (1970)
- Tejumola, H. O., 10.1007/BF02417936, Ann. Math. Pura. Appl. 92 (1972), 65–75. (1972) Zbl0242.34046MR0318615DOI10.1007/BF02417936
- Tunç, C., Çmar, I., On the existence of periodic solutions to nonlinear differential equations of second order, Differ. Uravn. Protsessy Upr. (Differential equations and control processes), 3 (2008), 1–6. (2008) MR2515107
- Tunç, C., Boundedness of solutions of a third-order nonlinear differential equation, J. Inequal. Pure and Appl. Math. 6, 1 (2005), 1–6. (2005) Zbl1082.34514MR2122950
- Tunç, C., 10.4067/S0716-09172009000200002, Proyecciones Journal of Mathematics 28, 2 (2009), 125–132. (2009) MR2529760DOI10.4067/S0716-09172009000200002
- Tunç, C., Some new results on the boundedness of solutions of a certain nonlinear differential equation of third-order, International J. of Nonlinear Science 7, 2 (2009), 246–256. (2009) Zbl1371.34045MR2496738
- Yoshizawa, T., Liapunov’s function and boundedness of solutions, Funkcialaj Ekvacioj 2 (1958), 71–103. (1958) MR0114981
- Yoshizawa, T., Stability Theory by Liapunov’s Second Method, The Mathematical Society of Japan, 1966. (1966) MR0208086
- Yoshizawa, T., Stability Theory and Existence of Periodic Solutions and Almost Periodic Solutions, Spriger-Verlag, New York–Heidelberg–Berlin, 1975. (1975) MR0466797
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.