scholarly journals On Partial Complete Controllability of Semilinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Agamirza E. Bashirov ◽  
Maher Jneid
Keyword(s):  
Differential Equation ◽  
State Space ◽  
Control Systems ◽  
Order Differential Equation ◽  
Sufficient Condition ◽  
Complete Controllability ◽  
Semilinear Systems ◽  
First Order ◽  
Partial Controllability ◽  
First Order Differential Equations

Many control systems can be written as a first-order differential equation if the state space enlarged. Therefore, general conditions on controllability, stated for the first-order differential equations, are too strong for these systems. For such systems partial controllability concepts, which assume the original state space, are more suitable. In this paper, a sufficient condition for the partial complete controllability of semilinear control system is proved. The result is demonstrated through examples.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 718 ◽  
Author(s):  
Emad R. Attia ◽  
Hassan A. El-Morshedy ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Oscillation Criteria ◽  
Lower Upper ◽  
First Order ◽  
Upper Limit ◽  
First Order Differential Equations

New sufficient criteria are obtained for the oscillation of a non-autonomous first order differential equation with non-monotone delays. Both recursive and lower-upper limit types criteria are given. The obtained results improve most recent published results. An example is given to illustrate the applicability and strength of our results.

scholarly journals Fractional differential equation with uncertainty

2021 ◽  
Vol 23 (08) ◽  
pp. 181-185
Author(s):  
Karanveer Singh ◽  
◽  
R N Prajapati ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
First Order ◽  
Fractional Differential ◽  
First Order Differential Equations

We consider a fractional order differential equation with uncertainty and introduce the concept of solution. It goes beyond ordinary first-order differential equations and differential equations with uncertainty.

scholarly journals A note on a paper of Bowcock and Yu

1989 ◽  
Vol 40 (3) ◽  
pp. 421-424
Author(s):  
I. P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
All Solutions ◽  
Necessary And Sufficient

Consider the first order differential equation (1) , where pi, and τi, for i = 1,…,n, are positive constants. To find necessary and sufficient conditions, in terms of the coefficients and the delays only, under which all solutions of (1) oscillate, is a problem of great importence. In a recent paper, Bowcock and Yu claimed that is a necessary and sufficient condition for all solutions of (1) to be oscillatory. In this paper a counterexample shows that the above result is not valid and the error in this paper is indicated.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

scholarly journals On the integration processes of A. Huťa

1963 ◽  
Vol 3 (2) ◽  
pp. 202-206 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Sixth Order ◽  
Order Accuracy ◽  
First Order ◽  
Runge Kutta ◽  
Image Position

Huta [1], [2] has given two processes for solving a first order differential equation to sixth order accuracy. His methods are each eight stage Runge-Kutta processes and differ mainly in that the later process has simpler coefficients occurring in it.

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