Research Article
Lyapunov-type inequalities for third order linear differential equations with two points boundary conditions
Abstract
In this paper, by using Green's functions for second order differential equations, we establish new Lyapunov-type inequalities for third order linear differential equations with two points boundary conditions. By using such inequalities, we obtain sharp lower bounds for the eigenvalues of corresponding equations.
References
- M.F. Aktas, Lyapunov-type inequalities for $n$-dimensional quasilinear systems, Electron. J. Differential Equations 67, 1-8, 2013.
- M.F. Aktas, D. Çakmak and A. Tiryaki, A note on Tang and He’s paper, Appl. Math. Comput. 218, 4867-4871, 2012.
- M.F. Aktas, D. Çakmak and A. Tiryaki, Lyapunov-type inequality for quasilinear systems with anti-periodic boundary conditions, J. Math. Inequal. 8, 313-320, 2014.
- M.F. Aktas, D. Çakmak and A. Tiryaki, On the Lyapunov-type inequalities of a threepoint boundary value problem for third order linear differential equations, Appl. Math. Lett. 45, 1-6, 2015.
- G. Borg, On a Liapounoff criterion of stability, Amer. J. Math. 71, 67-70, 1949.
- A. Cabada, J.A. Cid and B. Maquez-Villamarin, Computation of Green’s functions for boundary value problems with Mathematica, Appl. Math. Comput. 219, 1919-1936, 2012.
- D. Çakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput. 216, 368-373, 2010.
- D. Çakmak, On Lyapunov-type inequality for a class of nonlinear systems, Math. Inequal. Appl. 16, 101-108, 2013.
- D. Çakmak, M.F. Aktas and A. Tiryaki, Lyapunov-type inequalities for nonlinear systems involving the $(p_{1},p_{2},...,p_{n}) $-Laplacian, Electron. J. Differential Equations 128, 1-10, 2013.
- D. Çakmak and A. Tiryaki, On Lyapunov-type inequality for quasilinear systems, Appl. Math. Comput. 216, 3584-3591, 2010.
- D. Çakmak and A. Tiryaki, Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the $(p_{1},p_{2},...,p_{n}) $-Laplacian, J. Math. Anal. Appl. 369, 76-81, 2010.
- P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964 an Birkhäuser, Boston 1982.
- E.L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1926.
- W.G. Kelley and A.C. Peterson, The Theory of Differential Equations, Classical and Qualitative, Springer, New York, 2010.
- A. Liapunov, Probleme general de la stabilite du mouvement, Annales de la Faculte des Sciences de Toulouse pour les Sciences Mathematiques et les Sciences Physiques 2, 203-474, 1907.
- A. Tiryaki, D. Çakmak and M.F. Aktas, Lyapunov-type inequalities for a certain class of nonlinear systems, Comput. Math. Appl. 64, 1804-1811, 2012.
- A. Tiryaki, D. Çakmak and M.F. Aktas, Lyapunov-type inequalities for two classes of Dirichlet quasilinear systems, Math. Inequal. Appl. 17, 843-863, 2014.
- A. Tiryaki, M. Ünal and D. Çakmak, Lyapunov-type inequalities for nonlinear systems, J. Math. Anal. Appl. 332, 497-511, 2007.
- X. Yang, On inequalities of Lyapunov type, Appl. Math. Comput. 134, 293-300, 2003.
Year 2019,
Volume: 48 Issue: 1, 59 - 66, 01.02.2019
Abstract
References
- M.F. Aktas, Lyapunov-type inequalities for $n$-dimensional quasilinear systems, Electron. J. Differential Equations 67, 1-8, 2013.
- M.F. Aktas, D. Çakmak and A. Tiryaki, A note on Tang and He’s paper, Appl. Math. Comput. 218, 4867-4871, 2012.
- M.F. Aktas, D. Çakmak and A. Tiryaki, Lyapunov-type inequality for quasilinear systems with anti-periodic boundary conditions, J. Math. Inequal. 8, 313-320, 2014.
- M.F. Aktas, D. Çakmak and A. Tiryaki, On the Lyapunov-type inequalities of a threepoint boundary value problem for third order linear differential equations, Appl. Math. Lett. 45, 1-6, 2015.
- G. Borg, On a Liapounoff criterion of stability, Amer. J. Math. 71, 67-70, 1949.
- A. Cabada, J.A. Cid and B. Maquez-Villamarin, Computation of Green’s functions for boundary value problems with Mathematica, Appl. Math. Comput. 219, 1919-1936, 2012.
- D. Çakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput. 216, 368-373, 2010.
- D. Çakmak, On Lyapunov-type inequality for a class of nonlinear systems, Math. Inequal. Appl. 16, 101-108, 2013.
- D. Çakmak, M.F. Aktas and A. Tiryaki, Lyapunov-type inequalities for nonlinear systems involving the $(p_{1},p_{2},...,p_{n}) $-Laplacian, Electron. J. Differential Equations 128, 1-10, 2013.
- D. Çakmak and A. Tiryaki, On Lyapunov-type inequality for quasilinear systems, Appl. Math. Comput. 216, 3584-3591, 2010.
- D. Çakmak and A. Tiryaki, Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the $(p_{1},p_{2},...,p_{n}) $-Laplacian, J. Math. Anal. Appl. 369, 76-81, 2010.
- P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964 an Birkhäuser, Boston 1982.
- E.L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1926.
- W.G. Kelley and A.C. Peterson, The Theory of Differential Equations, Classical and Qualitative, Springer, New York, 2010.
- A. Liapunov, Probleme general de la stabilite du mouvement, Annales de la Faculte des Sciences de Toulouse pour les Sciences Mathematiques et les Sciences Physiques 2, 203-474, 1907.
- A. Tiryaki, D. Çakmak and M.F. Aktas, Lyapunov-type inequalities for a certain class of nonlinear systems, Comput. Math. Appl. 64, 1804-1811, 2012.
- A. Tiryaki, D. Çakmak and M.F. Aktas, Lyapunov-type inequalities for two classes of Dirichlet quasilinear systems, Math. Inequal. Appl. 17, 843-863, 2014.
- A. Tiryaki, M. Ünal and D. Çakmak, Lyapunov-type inequalities for nonlinear systems, J. Math. Anal. Appl. 332, 497-511, 2007.
- X. Yang, On inequalities of Lyapunov type, Appl. Math. Comput. 134, 293-300, 2003.
There are 19 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | February 1, 2019 |
| Published in Issue | Year 2019 Volume: 48 Issue: 1 |