# Instability of a Fifth-Order Nonlinear Vector Delay DifferentialEquation with Multiple Deviating Arguments

@article{Tun2013InstabilityOA, title={Instability of a Fifth-Order Nonlinear Vector Delay DifferentialEquation with Multiple Deviating Arguments}, author={Cemil Tunç}, journal={Journal of Mathematics}, year={2013}, volume={2013}, pages={1-5} }

We study a fifth-order nonlinear vector delay differential equation with multiple deviating arguments. Some criteria for guaranteeing the instability of zero solution of the equation are given by using the Lyapunov-Krasovskii functional approach. Comparing with the previous literature, our result is new and complements some known results.

## 2 Citations

### On the instability of nonlinear functional differential equations of fifth order

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- 2017

espanolEl autor presenta condiciones suficientes para la existencia de soluciones periodicas de dos ecuaciones diferenciales con retraso de alto orden. El enfoque tecnico se fundamenta en la…

### FURTHER INSTABILITY RESULT ON THE SOLUTIONS OF NONLINEAR VECTOR DIFFERENTIAL EQUATIONS OF THE FIFTH ORDER

- Mathematics
- 2015

FURTHER INSTABILITY RESULT ON THE SOLUTIONS OF NONLINEAR VECTOR DIFFERENTIAL EQUATIONS OF THE FIFTH ORDER

## References

SHOWING 1-10 OF 35 REFERENCES

### Instability of a Nonlinear Differential Equation of Fifth Order with Variable Delay

- Mathematics
- 2012

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for…

### An instability theorem for a certain fifth-order delay differential equation

- Mathematics
- 2011

Text of the abstract. The main purpose of this paper is to introduce a new instability theorem related to a flfth order nonlinear difierential equation with a constant delay. By means of the…

### A new instability result to nonlinear vector differential equations of fifth order.

- Mathematics
- 2008

By constructing a Lyapunov function, a new instability result is established,
which guarantees that the trivial solution of a certain nonlinear vector differential equation of
the fifth order is…

### Further Results on the Instability of Solutions of Certain Nonlinear Vector Differential Equations of Fifth Order

- Mathematics
- 2008

### On the instability of solutions of an eighth order nonlinear differential equation of retarded type

- Mathematics
- 2011

In this paper, we give some sufficient conditions on the instability of the zero solution of a kind of eighth order nonlinear differential equations of retarded type by using the Lyapunov direct…

### ON THE INSTABILITY OF SOLUTIONS TO A CERTAIN CLASS OF NON-AUTONOMOUS AND NON-LINEAR ORDINARY VECTOR DIFFERENTIAL EQUATIONS OF SIXTH ORDER

- Mathematics
- 2008

The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our…

### Instability theorems for certain fifth-order differential equations

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1978

1. Consider the constant-coefficient fifth-order differential equation: It is known from the general theory that the trivial solution of (1·1) is unstable if, and only if, the associated (auxiliary)…

### Instability results for certain systems of fourth and fifth order differential equations

- MathematicsAppl. Math. Comput.
- 2003

### On conditions of inversion of A. M. Lyapunov's theorems on instability for stationary systems of differential equations (Russian)

- Dokl. Akad. Nauk. SSSR (N.S.),
- 1955

### On conditions of inversion of A. M. Lyapunov’s theorems on instability for stationary systems of differential equations

- Doklady Akademii Nauk SSSR, vol. 101, pp. 17–20, 1955.
- 1955