scholarly journals CONSTRUCTION OF AN ANALOG OF THE FREDHOLM THEOREM FOR A CLASS OF MODEL FIRST ORDER INTEGRO-DIFFERENTIAL EQUATIONS WITH A SINGULAR POINT IN THE KERNEL

2017 ◽  
pp. 24-35
Author(s):  
Sarvar Kakgramonovich ZARIPOV ◽  
Keyword(s):  
Singular Point ◽  
Differential Equations ◽  
First Order ◽  
Fredholm Theorem

The Hopf bifurcation theorem in three dimensions

1977 ◽  
Vol 82 (3) ◽  
pp. 469-483 ◽  
Author(s):  
Peter Swinnerton-Dyer
Keyword(s):  
Hopf Bifurcation ◽  
Singular Point ◽  
Differential Equations ◽  
Limit Cycle ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Bifurcation Theorem ◽  
First Order ◽  
Range Of Values ◽  
First Order Differential Equations

AbstractThe Hopf bifurcation theorem describes the creation of a limit cycle from an isolated singular point of a system of first-order differential equations depending on a parameter. This paper describes a method for determining explicitly a range of values of the parameter throughout which the Hopf configuration continues to exist; only the three-dimensional case is described in this paper, but the method can be generalized.

First order over determined system with singular point

2007 ◽  
Vol 18 (1) ◽  
pp. 65-80
Author(s):  
Adel Nasim Adib ◽  
Nusrat Rajabov
Keyword(s):  
Singular Point ◽  
First Order

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.

On the Strong Stability of First-Order Operator-Differential Equations

2004 ◽  
Vol 40 (5) ◽  
pp. 703-710 ◽  
Author(s):  
D. R. Bojovic ◽  
B. S. Jovanovic ◽  
P. P. Matus
Keyword(s):  
Differential Equations ◽  
Strong Stability ◽  
Order Operator ◽  
First Order

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

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