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 An application of topological degree to the periodic competing species problem

1986 ◽  
Vol 28 (2) ◽  
pp. 202-219 ◽  
Author(s):  
Carlos Alvarez ◽  
Alan C. Lazer
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lower Bounds ◽  
Topological Degree ◽  
Upper And Lower Bounds ◽  
Species Problem ◽  
Competing Species ◽  
Right Hand ◽  
The Right ◽  
Stability Of The Solution

AbstractWe consider the Volterra-Lotka equations for two competing species in which the right-hand sides are periodic in time. Using topological degree, we show that conditions recently given by K. Gopalsamy, which imply the existence of a periodic solution with positive components, also imply the uniqueness and asymptotic stability of the solution. We also give optimal upper and lower bounds for the components of the solution.

scholarly journals Stationary States of a Delay Differentional Equation of Insect Population’s Dynamics

2015 ◽  
Vol 19 (5) ◽  
pp. 18-34 ◽  
Author(s):  
S. A. Kaschenko
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Order Differential Equation ◽  
Parameter Method ◽  
Stationary States ◽  
Relaxation Oscillations ◽  
Initial Equation ◽  
First Order ◽  
Two Delays ◽  
Nonlinear Mappings

Relaxation oscillations in a first order differential equation with two delays are considered. On the basis of a special asymptotic big parameter method the problem of studying dynamics of an equation is reduced to the analysis of nonlinear mappings. Each cycle of these mappings corresponds to a periodic solution of the initial equation with the same stability.

Periodic Solutions of a Singular Equation With Indefinite Weight

2010 ◽  
Vol 10 (4) ◽  
Author(s):  
José Luis Bravo ◽  
Pedro J. Torres
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Singular Equation ◽  
Indefinite Weight ◽  
Piecewise Constant ◽  
Second Order Differential Equation ◽  
The Stability

AbstractMotivated by some relevant physical applications, we study the existence and uniqueness of T-periodic solutions for a second order differential equation with a piecewise constant singularity which changes sign. Other questions like the stability and robustness of the periodic solution are considered.

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 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.

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