MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS

Elif Demirci; Nuri Özalp

doi:10.1501/Commua1_0000000693

MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS

Year 2013, Volume: 62 Issue: 2, 1 - 10, 01.08.2013

Elif Demirci Nuri Özalp

https://doi.org/10.1501/Commua1_0000000693

Abstract

By the help of upper and lower solutions, the monoton iterative
technique is applied to a coupled system of first order ordinary differential
equations with initial conditions depending on a function of end points. Some
existence and uniqueness results are obtained. An example for a predator-prey
system is given.

Keywords

Monotone technique, upper and lower solutions, existence and uniqueness, predator-prey

References

T. Jankowski, Ordinary diğerential equations with nonlinear boundary conditions. Georgian Mathematical Journal 9(2002), No. 2, 287-294.
G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone iterative techniques for nonlinear diğerential equations. Pitman, Boston, 1985.
V. Lakshmikantham, Further improvements of generalized quasilinearization method. Non- linear Anal. 27(1996), 223-227.
V. Lakshmikantham, S. Leela and S. Sivasundaram, Extentions of the method of quasilin- earization. J. Optim. Theory Appl. 87(1995), 379-401.
V. Lakshmikantham, N. Shahzad and J. J. Nieto, Methods of generalized quasilinearization for periodic boundary value problems. Nonlinear Anal. 27(1996), 143-151.
V. Lakshmikantham and N. Shahzad, Further generalization of generalized quasilinearization method. J. Appl. Math. Stochastic Anal. 7(1994), No. 4, 545-552.
V. Lakshmikantham and A. S. Vatsala, Generalized quasilinearization for nonlinear problems. Mathematics and its Applications, 440. Kluwer Academic Publishers, Dordrecht, 1998.
Y. Yin, Remarks on …rst order diğerential equations with anti-periodic boundary conditions. Nonlinear Times Digest 2(1995), No. 1, 83-94.
Y. Yin, Monotone iterative technique and quasilinearization for some anti-periodic problems. Nonlinear World 3,(1996), 253-266.

Year 2013, Volume: 62 Issue: 2, 1 - 10, 01.08.2013

Elif Demirci Nuri Özalp

https://doi.org/10.1501/Commua1_0000000693

Abstract

References

T. Jankowski, Ordinary diğerential equations with nonlinear boundary conditions. Georgian Mathematical Journal 9(2002), No. 2, 287-294.
G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone iterative techniques for nonlinear diğerential equations. Pitman, Boston, 1985.
V. Lakshmikantham, Further improvements of generalized quasilinearization method. Non- linear Anal. 27(1996), 223-227.
V. Lakshmikantham, S. Leela and S. Sivasundaram, Extentions of the method of quasilin- earization. J. Optim. Theory Appl. 87(1995), 379-401.
V. Lakshmikantham, N. Shahzad and J. J. Nieto, Methods of generalized quasilinearization for periodic boundary value problems. Nonlinear Anal. 27(1996), 143-151.
V. Lakshmikantham and N. Shahzad, Further generalization of generalized quasilinearization method. J. Appl. Math. Stochastic Anal. 7(1994), No. 4, 545-552.
V. Lakshmikantham and A. S. Vatsala, Generalized quasilinearization for nonlinear problems. Mathematics and its Applications, 440. Kluwer Academic Publishers, Dordrecht, 1998.
Y. Yin, Remarks on …rst order diğerential equations with anti-periodic boundary conditions. Nonlinear Times Digest 2(1995), No. 1, 83-94.
Y. Yin, Monotone iterative technique and quasilinearization for some anti-periodic problems. Nonlinear World 3,(1996), 253-266.

There are 9 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Elif Demirci This is me Nuri Özalp This is me
Publication Date	August 1, 2013
Published in Issue	Year 2013 Volume: 62 Issue: 2

Cite

APA	Demirci, E., & Özalp, N. (2013). MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 62(2), 1-10. https://doi.org/10.1501/Commua1_0000000693
AMA	Demirci E, Özalp N. MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2013;62(2):1-10. doi:10.1501/Commua1_0000000693
Chicago	Demirci, Elif, and Nuri Özalp. “MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62, no. 2 (August 2013): 1-10. https://doi.org/10.1501/Commua1_0000000693.
EndNote	Demirci E, Özalp N (August 1, 2013) MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62 2 1–10.
IEEE	E. Demirci and N. Özalp, “MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 62, no. 2, pp. 1–10, 2013, doi: 10.1501/Commua1_0000000693.
ISNAD	Demirci, Elif - Özalp, Nuri. “MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62/2 (August 2013), 1-10. https://doi.org/10.1501/Commua1_0000000693.
JAMA	Demirci E, Özalp N. MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62:1–10.
MLA	Demirci, Elif and Nuri Özalp. “MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 62, no. 2, 2013, pp. 1-10, doi:10.1501/Commua1_0000000693.
Vancouver	Demirci E, Özalp N. MONOTONE ITERATIVE TECHNIQUE FOR A COUPLED SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62(2):1-10.